Science of the Absolute Introduction to part one - Preliminaries
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Created on Monday, 20 October 2008 19:09
Last Updated on Saturday, 17 May 2014 13:50
Published on Monday, 20 October 2008 19:09
Written by Patrick Misson
THE SCIENCE OF THE ABSOLUTE
SCIENCE SEEKS CERTITUDE. A human being is naturally curious about two fundamental problems which are contained in the sentences: "Whence this world?" and "Who am I? When the first of these questions is kept in mind, we may be said to limit our enquiry to the visible world, perceived or perceptible. In its extended sense this domain can be said to comprise that of physics.
When one puts to oneself the question "Who am I?" one has to do so with the knowledge of factors which are not merely physical. One has to rely more on concepts than on mere percepts derived from sense data. One introspects or speculates on general ideas, mostly taken for granted by common sense experience. Such ideas are largely relied upon in the matter of arriving at any degree of certitude in metaphysics, which is the other aspect of knowledge, besides physics, under reference here. One's whole vision vis-a-vis the Physical world, together with one's own subjective experience, which is not experimentally demonstrable, thus emerges into view as the legitimate and unified basis of our present enquiry, containing the domains proper to physics and metaphysics. Physics is quantitative while metaphysics may be said to be qualitative. If physics gives primacy to space, metaphysics may be said to give primacy to time. if physics is phenomenal, metaphysics is noumenal. If physics is relative, metaphysics tends to look at this relative plurality in the light of something that is non-relative. When physics and metaphysics, thus understood, are treated unitively so that the certitude contained in the one helps the certitude contained in the other, by mutual verification, we have the beginnings of a Science of the Absolute.
The Science of the Absolute can also be called a Science of Sciences, a Unified Science, or an integrated body of knowledge. When such an enquiry is pushed further, so as to yield a common notion serving as a normative reference for all sciences, we then have a fully integrated Science of the Absolute.
Science, in its progressive and triumphant march, and as it is now understood, is faced with the problem of incertitude rather than the certitude which it thought it was gaining. The inductivo-hypothetical approach to the formulation of scientific laws or theories, based on calculations found permissible according to prevailing practices in mathematics, yields at present varying pictures of the physical world. Scientific myth-making is a danger to which we are becoming more and more exposed. When science is thus being allowed to part company with common sense, one becomes confused, both about what one should doubt as well as what one should believe. A normative or integrated notion of the Absolute, such as we have indicated above, can alone act as a regulative reference in this matter. Thus our attempt to give precision to the whole range of scientific thought is not a fanciful undertaking. Science, even as at present understood, consists of both conceptual and perceptual factors, being a mixture of calculations and observations.
1. THE NOTION OF THE ABSOLUTE
The notion of the Absolute has gone out of favour in the world of modern thought. This notion often leaves a bitter taste behind it when mentioned in the various contexts of modern life. In politics this bitterness is felt at its worst, as absolutism is quickly associated with totalitarianism, fascism, or dictatorship. The absolute religious authority of the Church has also contributed to this aversion, nay, horror, in the best of modern western minds. The excesses of the Inquisition and of witch-hunting, associated with the regime that has now been superseded by what is called the Age of Enlightenment or Reason, has given to scepticism a more dignified position than to any dogmatically authoritarian set of beliefs.
Modern humanity is still trying its best to shake off the after-effects of the nightmare of the Dark Ages, when the Pope wielded unbridled and arbitrary authority and, what is more, glaringly misused such authority. The one concern of modernism is to avoid a relapse into this outmoded way of thinking. The very notion of the Absolute, although implicitly taken for granted by almost all Western Philosophers, from Hume to Hegel, has begun to be at least explicitly discredited. Modern Philosophy is sometimes characterized as being non-absolutist and analytical. (1)
When we keep these modern prejudices in mind, we know in advance that the very title of the present work will raise doubt and suspicion about the tenability of even taking one's position on the side of the notion of the Absolute.
Our excuse for taking such a position is that modernism, especially progressive modern scientific thought, has made it imperative for us to drastically revise epistemological, methodological and axiological foundations, whether of philosophy, or science, or both.
2. UNIFIED SCIENCE KNOWS NO FRONTIERS
Unified science cannot recognize any frontiers, nor can it set itself any limitations between the various scientific disciplines, It must form an interrelated whole, with a proper absolutist epistemology, methodology, and axiology. It must also transcend the limits of language, tragically referred to in the Bible as "Babelization" or confusion of tongues. Parochial cultural values vary from one geographical unit to another. Linguistic frontiers exist between vernacular and vernacular. Tradition and custom also contribute to the crisscross patterns that cut across and divide common human understanding, making for many specialized and closed branches and sub-branches of their own The bane of compartmentalization and overspecialization of departments of knowledge is an impediment, rather than a guide, to a healthy and intelligent life.
Varied units, standards, norms and frames of reference are presently being adopted at random by specialists in the various branches of science. Double and multiple standards also prevail sometimes within the same discipline. The Special, the General, and the Unified Field Theories of modern relativity are examples of such a tendency. There are thus implied in many cases subtle violations of fundamental epistemological laws, often resulting in confusion between the arbitrary axiomatic convention in mathematical or logical thinking, and the actual experimental data to which they are meant to refer.
Conceptualism and perceptualism ought to lend validity to each other without either one being given exclusive primacy. The a priori approach and the a posteriori approach often interlace promiscuously making scientific literature sometimes resemble fable or even myth, and almost always violating the standpoint of common sense. A unified or normative Science, based on the notion. of the Absolute, can alone serve as a regulative factor to effect orderly integration of all branches of human enquiry. Thus it would be possible and necessary to transcend geographical, cultural and linguistic frontiers if anything like a Unified Science is to emerge at all. Without this, both physics and metaphysics treated unilaterally are bound to confuse the healthy sense of human values which alone can guide humanity purposefully and consistently to its natural goal.
An integrated Science of all sciences, implying both normalization of concepts and their renormalization with reference to the domain of percepts, has become in our time an imperative need; hence the justification for the present work. Modern progress in mathematics is opening the way more and more to the possibility of such a science.
3. THE STRUCTURAL UNITY OF THOUGHT
Modern trends in scientific investigation are revealing that certain striking common features are at once characterizing both the microcosmic and the macrocosmic worlds. Science is becoming more interested in description than in actual objective facts as unilaterally understood. Concepts thus gain more importance and what is more, the observer and the observed tend to belong together to a common context.
Thus cosmology and psychology are approaching each other, as it were, from opposite poles of the total knowledge-situation to which both belong. In such a process of integration of perceptual and conceptual aspects, physics and metaphysics have their equal share of importance on neutral ground. Quantum Mechanics relies on the same structure as is found in astronomy. Mathematics, logic and semantics are also revealing each day new parameters on the structural frontier which tend to conform to each other, as between disciplines previously considered to be different or distinct. Many modern books are beginning to stress the common structural aspect that underlies both the "subject-matter" and the "object-matter" of science. In the philosophy of science we have begun unconsciously to develop a science of philosophy, because of the common structural features that underlie both.
The logical form was known to Aristotle. Now we speak of logical frames, or matrices, which are valid and common as even between man and machine. Cybernetics and thermodynamics reveal structural features of a subtle subjective and selective order, all of which are capable of being treated together as constituting one startling development in modern scientific thought. It is now within the reach of thinkers to build a Unified Science, such as this present work is interested in.
Electromagnetism now occupies the central place once occupied by Newtonian Mechanics. Qualitative geometry is now replacing the purely quantitative one. Post-Hilbertian notions of the groundwork of both algebra and geometry are revealing new possibilities in which mathematics, as an independent science, becomes self-sufficient in matters relating to certitudes in both domains. Algebra can support geometry and vice-versa.
Thus we live at a time when far-reaching possibilities are opening before us. This in itself is encouraging enough to embolden us in our present undertaking. The common structure to which subjective thinking and objective events can be referred to for normalization and renormalization, in view of the certitude coming from both the perceptual and conceptual sides of human understanding, is perhaps the one most encouraging sign of our times. Sir Edmund Whittaker says this about renormalization:
"The development of quantum electrodynamics has, in fact, shown the necessity for what is called renormalization, which is precisely a recognition of this difference between the observed and the theoretical values of e and m .... Although Eddington did not live to see the development of this modern practice of renormalizing e and m, he said that a situation of this kind must arise and he uttered a warning against expecting too close an agreement between his theoretically calculated values and those obtained by measurement" (2)
This makes it possible to have a Science of the Absolute which previously we did not have.
4. LABORATORY KNOWLEDGE VERSUS SEMINARY WISDOM
A subtle, though tragic element of paradox lurks within the structure of thought. Only a normative study of the Absolute can bring this to light. There are two dichotomous aspects, two distinct poles, sometimes called antinomian principles, with a complementarity and ambivalent reciprocity between them, evident when the total knowledge-situation is reduced to its most simple, abstract, and general terms. They are based both on its conceptual elements on the one side, and its corresponding perceptual image on the other. These two join schematically in the core of human consciousness.
It is here, as it were, that from opposite sides of a subtle parameter, algebraic thinking may be said to meet its own dialectical counterpart made up of pure geometrical elements, entities or things. To transcend this tragic element, implying paradox, has been the major task of philosophy and is also the central problem which we have to face here.
The polemical battles that have raged between those who stressed concepts at the expense of percepts, and others who stressed the opposite, have raised and are still raising in our own time, clouds of controversy which contribute to fill libraries with more and more verbose books of vain speculation. Even today, such rumblings do not tend to abate. There are those like A.J.Ayer, who will too readily take one side and assert that metaphysics is 'nonsensical' and without significance (3) and that humanity can live wholly with the help of empirical knowledge and propositions based on it.
These are empirical, positivist, and analytical philosophers, variously called functionalists, operationalists, or pragmatists. In such a company we can also include instrumentalists, even when the instrumentalism implied by them is only logical or mathematical. Such philosophers tend to expect the whole truth to emerge to view one day when what are called the laboratory methods of science are pushed forward more and more scientifically. As they understand it, this is to be accomplished by piecemeal and trial-and-error methods until, by a gradual process of annexation of new ground, the unknown is brought within the scope of the known.
They then expect to triumph finally in creating a philosophy which would fully retain what they would prefer to call its "scientific" status. Such a dream is like that of a promised land; one which does not seem to recognize the paradox lurking at the core of truth, but rather tends to bypass it by a one-sided approach.
When unitively, structurally and schematically examined, such laboratory-biased scientists may be seen to be not fundamentally different in their one-sidedness from those in the rival camp who belong to the context of the wisdom of the seminary. Between these two rival worlds there is only an apparent outer contradiction. When the nature of this apparent opposition is more closely examined and intuitively understood, we come to realise the truth common to both, and then it is that the legitimate claims of a possible Unified Science of the future will come more clearly into view.
When Shakespeare said that one may call a rose by any name, yet it will still smell as sweet, he was putting his finger on the very tragic or paradoxical core of the total knowledge situation while trying to overcome the contradiction. Names are nearer to concepts, while smell belongs to the opposite pole of the world of percepts; both belong to the rose. The promiscuous mixing of these aspects leads to the confusion of tongues known as "Babelization" of which the natural consequence is a vain and voluminous verbosity often mistaken for good metaphysics. Unilateral approaches whether to physics or to metaphysics, are both wrong. One necessarily presupposes the other, and to learn how to give to each its due place in speculation is what we call the normative, unified, or unitive approach. The a priori approach is anathema to the physicist. Even phenomenologists of modern times, who stem out of Kantian and Hegelian idealism, have a secret repugnance of anything that savours of the a priori.
Husserl writes the following:
"I avoid as far as possible the expressions a priori and a posteriori, partly on account of the confusing obscurities and ambiguities which infect their ordinary use, but also because of the notorious philosophical theories which, as an evil heritage of the past, are interwoven with them." (4)
There are positivists or empiricist of our own time, like Bertrand Russell, who are becoming more and more conscious of the limitations of empiricism, especially because quantum mechanics has dealt a death blow to their programmes. A theory of knowledge accommodating quantum mechanics and electromagnetics with time, space, gravitation, and the principle of causality in the unified field of nature, or in the name of a continuum where space and time enter on equal footing, is in the process of being discovered by modern scientific thinkers. When they come nearer to their objective it could be expected that they will be able to shed their long -standing prejudice against the a priori synthetic approach of philosophers like Kant. By insisting on only the a posteriori analytic, they will never be expected to resolve the paradox. Only when this happens will it be possible for strict thinkers to have a complete bilaterally understood or reciprocally balanced theory of knowledge serving as a regulative principle for the normal progress of human knowledge.
Theologians may be charged with being dogmatic a priorists, who are ready to believe anything, even though wholly indemonstrable and thus unscientific in the usual sense. Those who belong to the seminary school of thought can have legitimately laid at their door many grave errors of omission or commission. This does not mean, either, that all truth is to be sought solely from the custodians of the laboratories.
There is a large body of general ideas taken for granted by the simplest of human beings, just because they happen to be human. The importance of general ideas in any total, yet strictly scientific scheme, should not be overlooked. When a child of two or three is watching an elder playing hide-and-seek with it, a third person observing the features of the child could notice an alternating play of expectation and dismay, hope or despair, suggesting a tendency alternately to scepticism, and to a willingness to believe. The child could be seen to be torn between the world of the visibles and the world of general ideas, both of which exist together only in the core of its absolute tabula rasa, as Locke said, constituting its normal consciousness.
When the hiding elder is not seen for a minute longer than expected by the child, one could see sadness and disappointment, ever growing stronger, reflected in its face. When the hiding face reappears, the wonder of it becomes too much to be contained by the little heart of the child. Here, in such a situation, the child's spirit swings, as it were, alternately between scepticism and belief. If we should substitute philosophers and scientists for the alternative realms of scepticism and belief possible to the child's mind, we would get a picture of the same total scope and alternating movement at the core of the bipolar paradoxical total knowledge situation which we have already tried to explain. We shall not go further into this question, however, because of having gone into such matters more thoroughly in previous studies.
Einstein is a good example of how mysticism itself is being included within the scope of science, as the following quotation shows:
"The most beautiful and most profound emotion we can experience is the sensation of the mystical. It is the sower of all true science. He to whom this emotion is a stranger, who can no longer wonder and stand rapt in awe, is as good as dead.
To know that what is impenetrable to us really exists, manifesting itself as the highest wisdom and the most radiant beauty which our dull faculties can comprehend only in their most primitive forms - this knowledge, this feeling is at the centre of true religiousness" (5)
If one makes a statement such as "All men are mortal", and one has the alternative of choosing the laboratory or the seminary for verifying the validity of the statement, common sense might tell us that it is not the laboratory one resorts to, but rather the seminary which normally deals with most general ideas, such as eternal life, etc. In the laboratory one can, at best, expect verification of such a truth by means of experiments with rats or rabbits in which they might die, or be killed, not all together, but on an average duration corresponding to the expectation of life proper to each species of animal. Proverbial wisdom does not, however, emerge in this manner. Statistical averages referring to the expectation of life have only a theoretical status, as "unreal" as in any metaphysical statement. That statistics tell lies is also a proverbial joke. If theologians cannot be trusted as the custodians for general ideas because of their past sins, where then have we to look for conformation, and the formulation of general ideas so desirable for all correct speculation?
General ideas do have their own valid source, although such a source is, at present, at least in the West, for many historical reasons, not fully relied upon, or acceptable to the mind of modern man. A priorism and absolutism have thus become notions which are non grata to the scientist. The decisive factor in our choice between seminary wisdom and laboratory knowledge consists in being able to transcend that tragic element of paradox hiding between the name of a rose and its own perfume, already referred to. They belong together to one and the same significant value-reality, truth, or fact.
5. CONCEPTS AND PERCEPTS AT LOGGERHEADS
If the mind is a tabula rasa, as assumed by Locke and other empiricists, it is not difficult to assume that there is a no-man's-land between concepts and percepts. These do not grow out of each other by any necessary sequence. There seems to be a strange gap between them. Percepts cannot be promoted to the status of concepts by straining our mind or forcing it into any kind of ratiocination. The very fact that children have to learn how to say "cat" and "rat" by a method called "look-and-say", so as to learn naturally how to bind percepts with their corresponding concepts, proves that there is a gap which has always to be bridged by a process of learning.
At the basis of what we have already referred to as "Babelization", or confusion of tongues, there is this element of strangeness as between names and forms. They seem to come to each other as if from opposite sides of the total knowledge-situation, normally consisting of the tabula rasa. While the empiricists might hold that percepts have primacy over concepts, thus minimizing the a priori element in human understanding, idealists and rationalists might do the opposite. It would be impossible to settle this dispute, because we can never observe what took place at the beginning. The case is similar to that of the primacy of the seed over the tree, or the egg over the chicken. For our purpose such an enquiry is both vain and unimportant. All we wish to underline here is the polarity between concepts and percepts, names and forms, the a priori and the a posteriori. As already indicated, if one is quantitative, the other is qualitative; if one is physical the other is metaphysical.
Thus, structurally speaking, a straight horizontal line tragically divides the vertical domain of purer thought. This line of demarcation has tragic implications. This is most evident with all its tribulations in courts of law, where it becomes most important that visual first-hand evidence strictly corroborate the various verbal statements made by witnesses. Even a simple road accident is best understood, and the guilty party most surely traced, when a sketch of the accident supports the verbal statement. Between the world of words and the world of visible events, there is room for all sorts of criminals and charlatans to thrive.
Even the apparent misunderstanding prevailing between people like Einstein, who say that observation is the final arbiter in the matter of scientific validity, and those like Kant, who give the a priori its full status independent of the a posteriori - which in effects divides the domain of thought into two rival camps, one called physics and the other called metaphysics - has its own raison d'être in this tragic gap subtly persisting between name and form.. The implied paradox between them has to be dissolved or made to fall if a normative Science of the Absolute is to emerge. Normalization and renormalization have to be applied correctly to one or other of the perceptual or conceptual aspects of reality, so that it is not a unilateral certitude we come to have, but a certitude that is verifiable from both ends, making it more final, ultimate, or absolute.
The best analogy to reveal the subtle reciprocity persisting between percepts and concepts can be derived from the contrast between light and darkness. These two cannot co-exist, in principle at least. Light implies something the opposite of darkness, and one cannot grow out of the other in direct quantitative proportion. Darkness can be more dark and brightness can be more bright.
The gap between them can be said to increase or to decrease, but the difference of qualitative content between them is intrinsic, and can be established by the normalization of the one in terms of the other, resorting to a principle of double negation or double assertion. These are some of the deeper aspects of the dialectical methodology to which we shall return later. Let us only note at present that concepts and percepts approach each other from opposite sides of a structurally understood total knowledge-situation, belonging to normal human understanding.
There seems to be a film tragically separating the world of percepts from its corresponding world of concepts, so that a stranger who finds himself in a country whose language he does not know is made helpless, even in the matter of buying the simplest items of food or drink. The entire surface of the earth is divided into units where this dumbfoundedness is equally enforced, to his disadvantage. This element of agony he shares with many other members of his race.
This situation comes into evidence distressingly when children have to learn lessons from wordy books. Such is the agony of the classroom to which children of all countries are perennially exposed. Even with grown-ups the same element of agony is present, though perhaps in a more diffused and unrecognized form. Many nuisible, humourous, or tragic situations or disasters in life have their fecund origin in this film or factor separating horizontally, as it were, the observable and the intelligible aspects of our common human existence. The importance of this tragic element is therefore not to be minimised.
6. THE AXIOMATIC ORIGIN OF POSSIBLE TRUTH
While there is a necessary connection between sense data (plain sensum) and the percepts formed in our minds, different names are possible between a percept and its corresponding conceptual aspect. The latter - that is the concept - has only a contingent relationship to the sense data. We have noticed the gap separating percepts and concepts. When this gap has been transcended and we have reached the other side where conceptualizing takes place in the mind, we find that here too there is a fixed relationship between concepts and their corresponding word or name aspect. Every word in the dictionary corresponds to its concept. The overall structure of mutual relation between sense data and percepts on the one side, and words and their corresponding concepts on the other, remains constant and complete.
We can here be helped by imagining two persons conversing at a distance. There is an inter-subjective and a trans-physical, or an inter-physical and trans-subjective exchange based on sensory-motor impulses, taking place in the conversation. The whole event, with its double aspect, can be reduced to a common schema moteur, as Bergson has done so masterfully.(6)
Without entering into any further details of this structure at this preliminary stage, it will suffice for us to notice for the present that in the total structural situation involved, there is a jump or gap existing vertically between ontological or immanent percepts and their own teleological or transcendental aspects called names or concepts.
In this, there is a subtle ambivalence, distinctly revealing two poles. The pole of possibility, or of all possibilities, is recognized as the a priori, where axiomatic thinking has its fullest validity. At the other extreme of the same vertical axis, we can locate a corresponding pole where, instead of axiomatic thinking, we have mutual exclusion between given sets of sense data. This can be called the source of a posteriori thinking. Thus, we come back to the nominal, which is at the basis of the sentence; "One can call a rose by any name," and the actual, which refers to its smell; "it will smell as sweet," linked into a complete situation so as to reveal its ambivalent aspects. Here we have axiomatic thinking residing at the top pole, and necessity to exclude contradiction, as between actual aspects, at the bottom pole.
We have entered in preliminary fashion into these interrelationships between sense data, percepts, concepts, and names or words corresponding to them, so as to bring into relief the other pole which is not represented by what we have called the perceptual or laboratory-centred source of knowledge. Axiomatic thinking does not originate in the experimental world proper to physics. On the contrary, all axiomatic thinking has, in full measure, the a priori implicit in it, and should therefore be delegated to that pole where general ideas originate within the structure of total human understanding. This can also be called the metaphysical or the ultra-physical. The conceptualized version of both the immanent and the transcendental aspects of reality could be comprised within the scope of this pure logical parameter. Descartes has marked clearly the limits within which metaphysical thought may be said to live and move, when he indicates in his Discourse on Method that cogito ergo sum is a natural starting point for all systematic doubting or speculation.
"Accordingly, the knowledge: "I think, therefore I am", is the first and most certain that occurs to one who philosophizes in an orderly (way)." (7)
He further adds that God is the source of all general ideas:
"When the mind afterwards reviews the different ideas that are in it, it discovers what is by far the chief among them - that of a Being omniscient, all-powerful, and absolutely perfect; and it observes that in this idea there is contained not only possible and contingent existence, as in the ideas of all other things which it clearly perceives, but existence absolutely necessary and eternal." (8)
Even if we find it necessary to avoid this theological second limit and prefer to call it by another name than that of God, it remains true all the same. There is an axiomatic source of all possible a priori thinking where all general ideas originate at the top of the vertical axis, lending support in a descending dialectical way to give validity to more or less possible ramifications of general ideas. Pure nominalism, where any name is as good as any other, gives full scope to the contingent element in thought. Names become more definitely understood or grasped through the meaning we have given to them by what we call concepts. There can be a hierarchy of concepts belonging to sets or sub-sets representing different grades of significant human values with their corresponding terms with which all dictionaries of any linguistic region are seen to be filled.
Word and meaning thus are coupled together as with two dictionaries with a one-one correspondence between them.
Corresponding to this descending ramification we can build up, from the necessary pole of existence, a ramification of perceptually ascending terms resembling a Tree of Porphyry. The ascending and descending ramified sets meet in a tragic no-man's-land, already referred to as the region where innocent school-children suffer boredom in their schoolrooms. We shall reserve further justification of these structural details for future treatment in their relevant context as they arise, but the rough outline has to be kept in mind from the very beginning, so that our further discussions could become easier to follow.
7. THE "SUBJECT MATTER" AND "OBJECT-MATTER" OF THIS WORK
It is necessary for us to give a precise idea regarding what this work is about. In short, it is concerned, as the title itself indicates, with the Science of the Absolute. The word Absolute has so far had only a vague content giving room to a great deal of ambiguity. Both tautology and contradiction find their place at the very core of this basically ultimate notion, as explained elsewhere in our writings. (9)
We have already tried, as far as we could, to fix in philosophical terms the content of the notion of the Absolute. We are more concerned in this work with giving it scientific precision rather than a merely philosophical, religious or mystical description.
Contemplative literature of all countries, whether Chinese, Upanishadic, Persian or European mystic, contains many helpful indications which can be kept in mind in order to arrive at the precise notion that we are seeking to fix. They contain subtleties or secrets, sometimes clothed in exalting or exaggerated language, relying on analogies derived from popular proverb, fable or parable, and sometimes even mythology, all tending to detract, to a greater or lesser degree, from their scientific character, depending on the mood of the contemplatives. The modern positivist approach has to develop its own sober style in keeping with disciplines such as logic, semantics or mathematics, each of which is receiving attention by modern thinkers. A Russian scientist and his American counterpart are now able to communicate precisely and scientifically on such subjects as nuclear physics and quantum mechanics.
The notion of the Absolute is normally within the reach of human understanding. The mystery hitherto surrounding it is only due to an epistemological paradox which has to be shed, dissolved, abolished or banished from our way of thinking. Then a content can emerge from behind it, as it were, helping us to give precise significance even to such a subtle and ultimate notion.
The nature of the paradox itself needs much research to lay it bare, so as to enable us to fix the varying levels of perception or conception, analysis or synthesis within the limits of which it can reside. The possible number of such levels are many. We to reserve their enumeration for a later stage. (10)
Meanwhile, we can avail ourselves of the rich indications, some of which conform to scientific requirements, found in a vast body of contemplative literature generally known as the "Perennial Philosophy". They sometimes lend themselves admirably to structural analysis, and sometimes we can also discern in them traits of a special mystical language based on proto-linguistic characteristics. What Leibniz dreamt of accomplishing through the universal mathematics found in his writings could be of interest to us, as also what is cryptically suggested in texts such as the Upanishads, some of which we have examined elsewhere.
It is not impossible either, that even when clothed in mythological language certain scientific, subjective or structural verities do reveal themselves in writings such as the Upanishads, which by themselves constitute a vast body of literature devoted to the one aim of giving content or meaning to the Absolute. No particular one of these traditions is more important to us than another in the present work. We have to be free to benefit from all of them, especially where indications conform to the requirements of the scientific approach to which we are committed in advance. Our attitude is one that avoids exaggerations and exaltations though these are natural enough to the mystic. Closed loyalties to static religious forms of belief or behaviour are also avoided.
Our basic dictum is that a normative notion of the Absolute is within the reach of human understanding as given to humanity anywhere in the world. Such attainment of the Absolute is very natural to man, although requiring intense intellectual research on his part. The a priori and a posteriori approaches to truth or knowledge have to be made to come together from opposite poles, as it were, to meet on common ground. Concepts must marry their corresponding percepts, and in the resulting fusion paradox is abolished. A process of normalization and renormalization in a reverse sense is implied here. When the paradox, which could only be schematic and nominal in its status becomes wholly transparent to itself, the Absolute reveals itself in all its unified or unitive significance. It then becomes a powerful instrument for certitude in the domain of thought. It affords a fecund frame of reference for regulating all precise thinking, which would then gain a beauty of its own, forever and everywhere enhancing its value in the cause of human understanding.
8. THE STATUS, CONTENT AND SCOPE OF THE ABSOLUTE
The Absolute is not a thing nor is it a mere idea. When the philosopher has correctly located the paradox lurking between appearance and reality, the paradox itself tends to be abolished into the Absolute. The Absolute is a neutral notion in which all real things and all possible ideas about them can be comprised without contradiction or conflict. Thus, it is both a thing and an idea at once. Truth, reality, fact or existence refer to aspects of this central neutral notion named for convenience, the Absolute.
All notions or entities, from the most gross or tangible to the most subtle, reside at the core of the Absolute without rivalry.
They are absorbed unitively into its being and becoming. It is hard to give a definitely fixed status to the notion. Existence, subsistence and value factors are inclusively comprised in it, and as for its own reality, the question itself should not arise when the perfect neutrality of its status is once admitted. All dualities are to be dropped before the Absolute can be comprehended. In the context of the Absolute, even the faintest duality has to fade away into something which can even be said to be nothing. Whatever duality may still be suspected, it must be laid at the door of the limitations of human understanding, in its attempt to attain an ultimate notion of the Absolute. We have to admit this by the very validity of the general ideas based on human understanding which can be presupposed by us. More on this argument later. A truth that is not understandable can have no significance to man, and, conversely, what is merely significant to him, as it were, from this side, will, by that very reason not fully attain to any absolute status. Half of such a conviction at least has to come from direct or indirect human experience, but the other half has to depend on the descent from above of general ideas, in the overall situation of human enquiry into the totality of which everyone of us is born. There is a double process, with both the aspects of endosmosis and exosmosis involved in the overall process of human understanding.
One does not educate oneself merely by everyday experience, but is obliged, consciously or unconsciously, to accept general ideas which are sometimes most elusive, because of their being axiomatic in character. Throughout this work we have to remember this bilateral nature of the progress of human thought.
It is said that primitive religion begins with the fear of natural forces affecting simple human life. This fear foisted on to so-called primitive man can easily grow into a wonder, rather than a fear, when the "man in the street" is kept in mind. When we think of still more civilized individuals we might use the term "natural curiosity" for the same element of the desire to know. Man naturally seeks to dispel all doubts, some of which are more proper to immature persons rather than to would-be philosophers. Whatever the grade of curiosity involved, the satisfaction has to take place from both the poles of the knowledge-situation we have referred to. There is both a descending and an ascending dialectical process involved, and what we call certitude is a resultant of the meeting of experiences and valid expectations, as well as probabilities and possibilities, all lending apodictic or dialectical certitude to each other. The quest is only satisfied when such a meeting takes place. Neither the inductivo-hypothetical approach nor the unmethodical reliance on the a priori, where all general ideas reside, can bring the final conviction of absolute certitude. Absolute science must seek such an absolute certitude. Epistemologically, the Absolute has only a nominalistic and schematic status.
9. THE TERM "ABSOLUTE" WIDELY USED BY SCIENTISTS
Even scientists who are normally against absolutist notions have much use for this term in its varying connotations or denotations. We know of terms like absolute zero temperature, which is a kind of ultimate limit in the measurement of heat. Independent, self-sufficient, pure, unchanging or constant factors wherever they come into scientific discussion, are often referred to as being absolute.
If we take the notion of space in Euclid, so important to classical mechanics, we see that it is now condemned as unsatisfactory, because of its being an absolutist notion. Whether pure space can be called absolute or not is an open question, although from a common-sense standpoint it is generally taken for granted. The nature of space and its ultimate status for the scientist is one of those questions about which there is much vagueness prevailing at present. Relativistic space is not rigid and admits of some qualities such as curvature or elasticity. On the one hand we find that while Einstein strongly condemns Newtonian ideas of space as absolutist, he openly admits on the other hand that his own frame of reference for his special Theory of Relativity is as absolutist as that of Newton:
"With the discovery of the relativity of simultaneity, space and time were merged in a single continuum in the same way as the three dimensions of space had been before. Physical space was thus increased to a four-dimensional space which also included the dimension of time. The four-dimensional space of the special theory of relativity is just as rigid and absolute as Newton's space." (11)
The layman endowed with good common-sense has reason to complain that the term "absolute" is arbitrarily used here, and he can even suspect that he is being let down. Theologians do the same with gullible minds in the domain of belief.
We do not know, for example, whether we have to consider space as tending to become more absolutist or relativist in character when it is given a Lobachevskian or Riemannian matrix or structure, or even in the notion of a space-time continuum brought into use after Minkowski. If we think of time instead of space we find that the simultaneity of two events is summarily excluded from the way of thinking adopted by Einstein. This might be because the notion of time will too easily attain an absolute status if simultaneity of events in space is admitted by the relativist. Space has to be measured both by its character of vacancy as by its capability of being filled with something real or tangible, at one and the same time.
"If two bodies are of equal value for the filling of one such interval, they will also prove of equal value for the filling of other intervals. The interval is thus shown to be independent of the selection of any special body to fill it; the same is universally true of spatial relations. It is plain that this independence, which is a principal condition of the usefulness of framing purely geometrical concepts, is not necessarily a priori. In my opinion, this concept of the interval, detached as it is from the selection of any special body to occupy it, is the starting point of the whole concept of space.
Considered, then, from the point of view of sense experience, the development of the concept of space seems, after these brief indications, to conform to the following schema - solid body; spatial relations of solid bodies; interval; space. Looked at in this way, space appears as something real in the same sense as solid bodies." (12)
The paradox involved here is glossed over by modern relativists who do not wish to characterize pure space either as relative or absolute in status. They prefer rather to pin their faith on light, which can be considered as something perceivable and actually visible, such as the flashes of light whether in corpuscular or wave form emitted from the most distant of stars. Even after the failure of the Michelson-Morley experiment, revealing the astounding fact of the total absence of any ponderable ether, postulated by classical physicists as a sort of substitute for some absolute medium for light to travel through, modern physicists refuse to recognize any kind of space with an absolutist character. The above epoch-making experiment has laid bare the fact that light travels at an enormously high velocity, ungraspable to common-sense experience and, what is more, that the relative speeds or positions of the observers or the motion itself of the source of light that they observe do not in the least affect this factor referring to light in its power to fill all space.
One hears such statements as "thousands of light years" for a ray of light to travel from a distant star before it reaches an observer on earth. (13) Three-hundred thousand kilometers per second has to be multiplied many times by time units before common-sense is able even to think of such a supposedly perceivable physical event.
The person of common-sense has a right to object to the physicist who claims, even here, that this ray of light comes within the scope of perceivability which is the single condition dividing physics from metaphysics. The physicist thus rudely shocks and violates norms of common-sense thinking, wanting the poor "man in the street" to believe in fables not less far-fetched than those sometimes woven by theologians. Because physicists do not want to give an absolutist status to pure space they prefer to give more importance to the velocity of light, which they characterise by the less pretentious, yet synonymous term "constant".
If we come to examine impartially what this term "constant" is meant to imply to a normal man, who is neither prejudiced in favour of physics or of metaphysics, it is easy to see, in the independent, pure and ultimately phenomenal status of the velocity of light, the rudiments at least of a notion participating both ways. This could be either as an actuality or as an analogy, bridging, as it were, the intellectual gulf separating the domain of physics from that of metaphysics. In fact such expressions as "the light of the world", as used in theology, justify such a two-sided participation or transparency between the twin aspects involved here. The transition between the mental and the physical is a problem to which we shall be returning more than once in this work. Meanwhile, all that we wish to indicate here in advance is that instead of calling the velocity of light a mere constant for physics, it is justified to give light a more central place, having at one and the same time both a perceptual and a conceptual status in the context of the normative Absolute.
The term "absolute" as used by scientists undoubtedly leaves room for much clarification and precision. Space and time can be integrated more intimately than suggested by Minkowski, who, at best leaves the notion in the form of an amalgam of space-like and time-like factors. He gives primacy to space for purposes of physics, rather than to time which would necessarily compel them to be included under the inner life experience of metaphysics. How such an integration is possible will become more and more evident as we proceed.
10. DIALECTICAL IMPLICATIONS OF THE CONTENT OF THE ABSOLUTE
Relativity and absolutism are antonymous. One depends for its meaning on the other, and it is impossible to think of any theory of relativity without assuming its own inevitable dialectical counterpart. The observed fact of relativity does not need any theory to support it. Every schoolboy can be easily taught that when one or more trains on a railway platform move we witness in familiar terms the relativity of movement.
When this simple brute aspect is elevated to the full-fledged status of a theory, applying to the whole of the physical world, we are compelled to look for a mental frame of reference in respect of which this relativity can stand revealed, in the same way as a pillar on the railway platform acts as a reference for the schoolboy in appraising the relativism with which he is faced. Because the earth itself happens to be in motion, this reference to the actual pillar of the railway station has to be considered defective in an extended sense in the direction of which any theory of relativity might have to be developed.
If a schoolboy asked why the Empire State Building did not tumble down after he "proved" Newton and Euclid wrong, Einstein would be compelled to use many ambiguous "ifs" and "buts" before finding an answer sufficiently convincing to the schoolboy. The factual aspect of relativity is what should properly belong to physics, because physics avowedly gives primacy to the visible or perceivable.
Of the two poles of certitude mentioned above it is the perceptual pole that properly belongs to the physicist. Perceived or perceptible aspects of physical phenomena must normally carry more conviction than theories, that are bound to be more and more conceptual, thus tending to be metaphysical rather than physical in status. The more one moves away from brute facts into what might be mathematically constructed, the more one's calculations tend to have a necessary metaphysical status.
Strangely enough the history and the origin of the modern theory of relativity reveal a reverse order of progression because they have, consciously or unconsciously, been given a philosophical status instead of being kept strictly within the limits of the practice of physics in the laboratory or observatory. It consists of more than one stage of growth marked by the Special and General Theories followed by an attempt at a Unified Field Theory, more generalized and absolute, if we may say so, than the other two. One remarkable feature of the origin of these theories is that it is on the failure of an experiment, rather than on its success, that the whole speculation or calculation started.
The Michelson-Morley experiment was expected to prove some ether-like substratum, acting as a ponderable or material medium for light to travel from one locality to another, however distant or near. Yet, in spite of its repetition, the experiment insisted on revealing the opposite of what was expected. Instead of boldly drawing the conclusions natural to this experiment, which would have perhaps compelled physicists to accept an immaterial medium for light to travel in, Einstein and others preferred to take backward steps and began to take refuge in what is now famous as the Lorentz transformation, consisting of a mathematical equation whereby the Fitzgerald contraction became verified. An equation is not a factual starting point but is itself based on arbitrary a priori and axiomatic considerations as in mathematics as a whole, whether algebraic or geometric.
Even a cow being chased out of a field by a gardener, may be said to be conscious of the fact of the relativity of motion. Thus leaving behind the brute fact of relativity, Einstein on the other hand backed out even from the natural consequences of the Michelson-Morley experiment. Still wanting to be true to physics rather than metaphysics, he built up three grand stages of his noble edifice, based on the presupposition of a principle of universal relativity for the whole of physics. When closely scrutinized, as Bergson has done in a whole work dedicated to this very question, it becomes completely evident to anyone of common-sense, let alone a philosopher, that he remains all through these theorizations true to fundamental Cartesian schematic notions, which have been acceptable to all rationalist philosophers in modern Europe.
We shall be devoting more space to an examination of these aspects because the claims of absolutism cannot be established without facing fully the serious implications and consequences of this theory, which has taken possession of all modern minds as a substitute philosophy.
Enough has been said for the present, at least to make it clear that this theory of relativity, seeming to loom so large in the modern mind, lends itself easily as a ready idiom to be flung against any absolutist way of speculation. Yet, the theory of relativity still rests on very tentative and unstable epistemological ground. The fact that Einstein has not fully succeeded in enunciating his Unified Field Theory is sufficient evidence of this. Concerning Einstein's inability to fully succeed with his Unified Field Theory, we read the following:
"Believing in the fundamental unity of nature, Albert Einstein worked on this problem continuously, reporting his tentative conclusions in an appendix to the 4th edition of his Meaning of Relativity (1953). His death in 1965 interrupted these labours." (14)
11. THE DIALECTICAL APPROACH TO THE NOTION OF THE ABSOLUTE
The Absolute can be attained in many ways. Some of them are more speculative and indirect, while others are simple and direct.
When we start from simple everyday experience and attain the core of the notion or the reality of the Absolute, we can be said to be most scientific in our approach.
In this respect there is a method of approach favoured by the Guru Narayana which seems to be very simple. He said that if we should think of a body it would be possible to divide it into parts and each part could be further subdivided, this process being continued ad infinitum, At the term of such a process, the quantitative aspect of the body concerned tends to get abolished and attains to a more qualitative status. In other words, the visible tends to become intelligible, having a mental or subjective, rather than an objective existence. When this notion remains in the mind and is further conceived independently and purely as a reality or notion sufficient to itself, we attain the Absolute. Other thinkers like Descartes have preferred to speculate on time or duration which is within the inner experience of every human being. Pure duration, according to Descartes, is God. By this he only means to say that it attains the status of the Absolute. He is not necessarily thinking of the theological God of the scholastic context. Thus we see two fundamental notions, one of matter occupying space, and the other of time filled with events, both of which when subjected to contemplative or scientific purification, can attain the Absolute in a most direct and simple manner.
Besides space and time, represented schematically after the manner of Cartesian correlates, we can think of cause as a third and very fundamental category. Cause implies effect and when related to the time axis it represents a link in a chain of successive alternating pairs of causes and effects. It is possible for us to think of this process of causes and effects as operating in this world both prospectively, and retrospectively.
The former is called imagination and the latter memory. At any given moment anywhere, and with anybody, there is an eternal present unequivocally established by philosophers like Plato and made acceptable to other philosophers.
Causality as a principle can further be abstracted and generalized by the human mind, being capable of such mathematical or scientific abstraction and generalization without knowing any limit. Herein lies the possibility of finding the central locus of all future scientific speculation, whether based on outer experiments or inner certitude. Thus, the principle of causality can be put on a pedestal of a universalized basis as functioning at the core of the process of becoming, to which the whole of the universe is subjected, as could be seen by all of us.
Even scientists like Max Planck have been obliged in recent years to give this principle of causality its full recognition and status, although such matters were, until recently, considered outside the scope of physics as belonging to the outmoded so called metaphysical way of thinking. Einstein has approved of Planck's stand on this subject and with such approbation on the part of the dean of modern scientific thought, it is fully permissible for us to say that the principle of causality has once again been elevated to an absolutist status.
Thus, Time, Space, and Causality, when each of them is given its capital initial letter, can be considered as attaining, each by its own right, the status of the Absolute.
This way of thinking has long been accepted in the Platonic tradition. Plato could similarly elevate notions such as Beauty by the purifying process of generalization and abstraction, going on, hand in hand, as it were, to the status of an absolute value, each by its own right.
Attaining the Absolute in this manner has therefore nothing unscientific nor unphilosophical about it when we further consider that causation, common as an abstract principle of life, lives in the heart of each of us, making it possible for us to live from one split second to another, causality itself being nothing. We can locate this Principle at the apperceptive core of all consciousness, whether it belongs to human, animal, plant or sub-organic life; giving it a fully psychological status. In the phenomenal world it goes without saying that the same principle has a cosmological status. Further, there is no objection in giving this same principle, when fully glorified, a theological status as Descartes and even Hegel have already done in philosophy. Max Planck's remarks here confirm what we have to say:
"Some essential modification seems to be inevitable; but I firmly believe, in company with most physicists, that the Quantum Hypothesis will eventually find its exact expression in certain equations which will be a more exact formulation of the law of causality.
The principle of causality must be held to extend even to the highest achievements of the human soul.
We must admit that the mind of each one of our greatest geniuses - Aristotle or Plato, Kant or Leonardo, Goethe or Beethoven, Dante or Shakespeare - even at the moment of its highest flights of thought or in the most profound inner workings of the soul, was subject to the causal fiat and was an instrument in the hands of an almighty law which governs the world." (15)
We now quote Einstein who wrote a foreword to Planck's book and is in complete agreement with what Planck said:
"I am entirely in agreement with our friend Planck in regard to the stand which he has taken on the principle. He admits the impossibility of applying the causal principle to the inner processes of atomic physics under the present state of affairs; but he has set himself definitely against the thesis that from this unbrauchbarkeit or inapplicability we are to conclude that the process of causation does not exist in external reality. Planck has really not taken up any definite standpoint here. He has only contradicted the emphatic assertions of some quantum theorists, and I agree fully with him. And when you mention people who speak of such a thing as free will in nature it is difficult for me to find a suitable reply. The idea is of course preposterous ..... Honestly I cannot understand what people mean when they talk about freedom of the human will." (16)
From the above discussion we are able to extract a schematic outline which will be of great linguistic help to us for our purpose. The essence of time is its continuity as a process, tracing itself on the purest of notions of duration and, as we have said, it can attain an absolute status. Space when schematized, on the other hand, whether thought of pluralistically or as being merely empty of plurality, can be represented, after the principle underlying Cartesian correlates, by a line at right angles to time. We can represent it to ourselves as consisting of a contiguous rather than a continuous line extending horizontally and numerically rather than qualitatively, grading into more and more virtuality or actuality as it traces itself on the abscissa, on the plus or minus side according to its location. Such a schematic representation must have its own correct degree both of subjectivity and objectivity, and has to be neutralized between these two opposites in the human mind at one and the same time. It is in the world of qualitative values that such a schema can hold good and not in the world of mere quantitative things.
Matter and mind have to attain here an equal degree of transparency between them to make participation between the two correlates possible on homogenous and neutral ground. Further aspects of this schematic representation will be elaborated later.
Here it might be in place to add that almost any fundamental notion can be subjected to the kind of treatment we have adopted above. In the first instance the notion can be subjected to abstraction and generalization, and then it can be fitted into a schema. The first part of the process can be recognized as belonging to mathematical symbolism as prevails in algebraic calculations.
The second way of abstraction and generalization corresponds rather to the method known to geometry. We know in analytic geometry, and more so in the modern post-Hilbertian algebra of geometry, that one discipline corresponds to the discipline of the other when. structurally or schematically understood. Thus we can take the notion of truth and give it a neutral normative status in the context of the Absolute.
When the Upanishads speak of the One Eternal Female, or of gods such as Vishnu or Siva (17), they tend as in Plato, to give such notions a fully normalized and absolutist status. There are however, slight epistemological asymmetries, implicit or explicit, in the standpoints natural to various philosophers. We have to make allowances for this when we are thinking of a fully corrected version of the same before they could be considered fully normalized, both from the algebraic and the geometrical sides. Each fundamental notion can be given its legitimate central value, whether considered as a reference or a referent for human understanding treated in its most all-comprehensive sense.
12. DIALECTICAL METHODOLOGY
Francis Bacon conceived of scientific method as consisting of experiment, observation and inference.
In his days science was thought of mainly as a laboratory discipline, and the tradition of earlier classical science, based on astronomy and on the wonders revealed by the telescope, had its own complicated theories in which calculations such as those of Kepler played a large part. By Bacon's time all that was extraneous and theoretical in the domain of science tended to be cut out and the main task of the scientist was to try different ways of putting together or taking apart visible things. This was what Bacon understood by experiments.
Modern science, on the other hand, relies largely on both calculations and observations at one and the same time. Euclidian and Newtonian ideas are not enough to satisfy the modern scientist. The inductivo-hypothetical method, having been accepted for scientific investigation, yields a large number of theories. Since the time of Newton and Euclid many of these theories have been subjected to drastic revisions. Classical physics has thus become more and more a stranger to modern physicists. Exactly how many classical ideas have been discarded by moderns, and how precisely other substitutes have been developed by them, still remain an open question.
The universal law of gravitation enunciated by Newton remains almost intact, in spite of the drastic changes in the theories of the structure of space and the relativity of motion brought about by modern scientific theories. The method proper to science has now changed and the roles played by analytical geometry and algebra are now very great. Mechanics has still to include rigid Euclidian or Newtonian frames of reference side by side with more subtle versions of the same, giving place within its scope to electromagnetics and quantum mechanics. These latter call for a more flexible basis on which alone they can have meaning.
In modern relativity and quantum mechanics we find a more central place being taken by mathematical equations instead of laboratory experiments. It is legitimate now to speak about a non-experimental science of the type Eddington stood for. Leading scientists now feel the inevitability of a thoroughgoing epistemological revision of the whole position of scientific thought. When epistemology is drastically subjected to revision, it is natural to expect that a corresponding methodological revision will also follow in its wake. Thus it is that many thinkers brought up on modern scientific ideas are beginning to adopt some new ways hitherto considered outside the scope of respectable scientific method.
Conclusions based on probability, being essentially statistical in character and therefore of questionable certitude, are now admitted as correct scientific findings. This is evident in quantum mechanics where the positions of particles structurally understood are fixed, even sometimes when not observable at all. They are treated as observed, from statistical laws of averages, with the possibility of grave incertitude, or indeterminism at the very core of science, which Heisenberg's principle has clearly brought out. The claims to exact and objective precision for the methods employed by scientists have now become highly questionable. It is interesting to note at this juncture how scientific thinkers, wanting to enrich and supplement the methods of science, are looking to other fields hitherto considered heterodox.
One striking example of this is the fact that they are beginning to speak of the dialectical approach which was, till now, considered taboo, belonging, as it were, to the other side of the barrier.
Marx and Engels, who employed dialectics for the first time after Hegel, were not fully favoured by those who belonged to the earlier group. Political and cultural prejudices tended to make them heterodox thinkers. Modern progress in scientific thinking, especially in the matter of an ever more imperative need to formulate bolder and bolder theories about the universe, now makes a reconciliation necessary. The dialectical approach is thus being made acceptable. The inductivo-hypothetical approach can no longer claim a high degree of certitude, even though it was considered good enough by scientists up to the present time. When statistical methods based on 'samplings' and 'probability curves' are thrown into the bargain, the position becomes even worse as far as scientific certitude is concerned.
A closer scrutiny of the epistemological implications of these two methods has made it evident, to some modern thinkers at least, that in essence the dialectical approach is not fundamentally different from what they have already accepted. Large trial-and-error samplings where probabilities are revealed as yielding vague degrees of certitude are not altogether unlike the certitude found in the Hegelian dialectical approach, where the thesis and the antithesis cancel out into a synthesis at a higher level. What the three levels, here implicitly taken for granted are, is a difficult question to resolve. The cancellation of thesis against antithesis in favour of a synthesis cannot even be imagined to take place except on the presupposition of an absolutist 'world-ground' or reality as its basis.
Thus by a long detour we are at present watching the strange phenomenon of orthodox scientists shaking hands with their worst opponents. When we remember that any dialectical methodology must presuppose some sort of absolutist basis on which alone it can become even ideologically understandable, we should be fully justified in thinking that modern scientists are already tacitly accepting the absolutist approach.
We have already referred to the hesitations of scientists. Even a scientist of the grade of Eddington had to be apologetic in the matter of suggesting some epistemological and methodological innovations of which he himself was a pioneer. We have already alluded to these elsewhere. It was he who first emphasized that concepts, not percepts, had to be given their important place in future scientific thought. In this conceptualizing and application of new mathematical norms and standards for scientific thought, he had to take care not to estrange his own opponents who remained more conservative and orthodox. Parochial limitations affect even the open domains of scientific thought and progress. In spite of science being an open and public discipline, cramping influences exist here and there, and sometimes come into evidence in an ugly way. In the matter of adopting a dialectical methodology we see the same hesitations and reservations, sometimes amounting to fear of opposition from the more prejudiced or conservative section within the same group.
We notice again a striking instance of the same pressure applied to another bold scientific thinker, Paul Freedham, who recently brought out a book entitled "Principles of Scientific Research".
It is sad to note how he has had occasion to complain, in the third person, as follows:
"Before proceeding further, a small digression is necessary. The author has been advised by his friends to omit the next few pages because they refer to scientific principles enunciated by two men whose names are now associated with bitter political controversies. Such an omission appears to him to be impermissible by standards of scientific honesty. If science, emancipating itself from theology, is to be enmeshed in political prejudices, then it is the duty of all honest scientists to combat such a disaster. The author believes that most of his readers will be with him in this attitude.
"The fundamental principles to which the author now proposes to refer without further preamble are those first enunciated by Marx and Engels." (18)
We can cite two others; the first is Vincent Edward Smith, who belongs to the Roman Catholic Thomist School of thought; and the other is Professor Karl R. Popper, whose affiliations are definitely pragmatic. Both tend to recommend, with their own particular reservations and hesitations, the adoption of dialectical methodology for science. It will be interesting for us to examine the reasons put forward by them so that we are able to bridge the gap existing in our own minds between the old inductivo-hypothetical reasoning and the dialectical methodology properly belonging to the absolutist way of thinking.
The former method has its affinity with the trial-and-error approach, having no methodic roots of its own. The Cartesian approach, by systematic doubting, from the starting point of cogito ergo sum, although more methodically sound, has closer direct reference to what we have distinguished as the metaphysical rather than the physical. In a unitive science combining both the physical and metaphysical, trial-and-error can supplement systematic doubting in order to make the methodology applicable to a more complete science. Probabilities and possibilities enter into the game, as it were, from the opposite poles of the a priori and the a posteriori. When the game between the two sides is played fully and freely we then have dialectical methodology. Let us first hear what Professor Popper has to say on the subject:
"If the method of trial and error is developed more and more consciously, then it begins to take on the characteristic features of 'scientific method' .... Criticizing and testing go hand in hand; the theory is criticized from very many different sides in order to bring out those points which may be vulnerable. And the testing of the theory proceeds by exposing these vulnerable points to as severe an examination as possible. This, of course, is again a variant of the method of trial and error .... Its success depends mainly on three conditions, namely, that sufficiently numerous (and ingenious) theories should be offered, that the theories offered should be sufficiently varied, and that sufficiently severe tests should be made….
"If this description of the development of human thought in general and of scientific thought in particular is accepted as more or less correct, then it may help us to understand what is meant by those who say that the development of thought proceeds on dialectic lines." (19)
He however makes the following reservation which brings out his hesitancy on the matter:
"From all this I think it is clear that one should be very careful in using the term 'dialectic'. It would be best, perhaps, not to use it at all - we can always use the clearer terminology of the method of trial and error." (20)
The subtle relationship between what is probable and what is actually proved, is masterfully analyzed by Professor Vincent Edward Smith, as we shall presently see. Probability, he points out, has to be accepted by the mind before actual proofs can be advanced. The former resides in the domain where dialectical reasoning is valid, while the actual inductions are made probable in the more realistic stratum of scientific findings. The following extracts will help to show how he accepts dialectical reasoning:
"Now the questions we raise and the consequences we deduce from various possible answers to our questions are not in themselves propositions about the real world. They do not become propositions about the real until the consequences are tested by induction. Until this induction takes place, dialectical propositions are provable only; by the subsequent induction they are proved .... "
"A proposition about reality is secured when, leaving the dialectical or logical level, we go to physical things and make an inductive test to see which consequence fits observed fact.
Demonstration deals with propositions about real causes and real effects. Dialectic, as such, deals only with logical beings.
Dialectic is a logic of questioning. A dialectician proposes possible answers to the questions he raises about any subject proposed to him. He then works out the consequences that follow from answering each question in an affirmative or negative way .... In contrast to the dialectical questioning that precedes it, induction is an operation of quite a different sort. It puts the mind in correspondence with the real.
To the extent that an investigator is still engaged in the dialectical preliminary to induction, his conclusions are probable but not yet proved. If the quest for nature's first principles is inductive because the principles cannot be demonstrated without using them, our induction to the principle must nevertheless be prefaced by a suitable dialectic. However, the dialectic yields only provable conclusions, which can be shown to be certain only by induction." (21)
Here the writer stands for a conditional dialectical approach.
A more thoroughgoing recognition of the dialectical approach is found in Paul Freedham, whom we have already quoted. He is bold enough to face his opponents land has clarified the situation, as follows:
"One may hope that a time will come when Engels' "Dialectics of Nature" will be removed from political book-shops and put on the shelves of those devoted to scientific publications. Needless to say, the fundamental principles enunciated by Marx and Engels do not supercede all previously discovered principles of scientific research, or invalidate other principles discovered at a later date. They can in no way serve as exclusive guides to such research, any more than any great scientific discovery can give a complete knowledge and understanding of the whole Universe. But they are of the utmost importance." (22)
He goes on further, elaborating the principles of Dialectical Materialism, tracing certain aspects of this method back to the times of Heraclitus:
"Of the four principles embodied in Dialectic Materialism, the first is that everything in Nature has a history, nothing is eternal and immutable, and everything is in a continued state of change. This principle, although first enunciated in this all-embracing form by Marx and Engels, had been formulated in more limited forms long before them. It was first propounded by Heraclitus, and found expression is the works of Bacon, Descartes and Leibniz, in Niels Stensen's theory of the possibility of tracing the history of the Earth through fossils, in Kant's cosmogony, and in the evolution theory of Lamarck. In the twentieth century this principle has been extended by Lemaitre and Dirac, and particularly by Milne." (23)
He continues, showing in detail the other principles found in Dialectic Materialism, and how scientific experiment has confirmed them:
"The other principles embodied in Dialectic Materialism, which, according to Marx and Engels, must be accepted by any scientist, consciously or unconsciously, in the framing of a correct hypothesis or final induction, are Unity of Opposites, Change of Quantity into Quality, and Negation and Negation of Negation.... According to the principle of unity of opposites, however, the only correct theory would be one which could unify the two conflicting theories. The present theory of light, which confirms the correctness of both the corpuscular and wave concepts .... is therefore a striking confirmation of the correctness of the 'unity of opposites' principle.
The principle of transition of quantity into quality is perhaps most strikingly illustrated in the case of radioactivity, when the mere quantitative increase of U 235, or of plutonium, above a certain critical point, suddenly produces a nuclear fission of the entire aggregate with liberation of enormous quantity of atomic energy.
The principle of negation and negation of negation is perhaps most impressively illustrated in astrophysics by the supernova phenomenon. According to the modern theory of stellar bodies, increase of mass beyond a certain point produces a decrease of volume .... Increase of mass thus negates the volume that mass may occupy, and beyond a certain point uncontrollable contraction to a geometrical point sets in. According to the principle of negation, however, such a state of affairs cannot exist without creating an opposite tendency, a factor which tends to, and at a certain point actually must, negate the negation .... This is what has actually been observed, when Zwicky discovered a number of supernovae." (24)
Finally, he sums up as follows:
"The primary value of the principles of unity of opposites, of change of quantity into quality, and of negation and negation of negation, from the point of view of scientific research, must reside in their value as guides to formulation of correct hypothesis .... It may be said, that on the whole, the possible value of dialectic materialism as a guide to scientific research is almost unexplored." (25)
Thus dialectical reasoning which supposedly originated in the so-called idealistic absolutism of Hegel has now found its legitimate place at the very heart of realistic and even experimental scientific thinking. We do not accept the term "Dialectical Materialism" which seems to tamper with the perfect interaction of thesis and antithesis by touching as it were only one scale of the balance when something is being weighed. We do accept, however, that there is a method of thinking which gives equal primacy to the immanent and transcendent aspects of truth, the implications of which we shall presently clarify.
13. CERTITUDE RESIDES AT THE CORE OF CONSCIOUSNESS
There are various kinds of logic, ratiocination or inference possible in scientific or speculative reason. Syllogisms which descend or ascend between generalities and particulars are meant to yield various degrees of certitude. There is always a middle term whereby certitude is established, whether in its ascent or in its descent.
Induction and deduction are processes of thinking pointing in opposite directions. Logical and mathematical calculations resemble each other in the reasoning process taking place within the mind. What is called proof or certitude is not a tangible thing, but refers to actuality or reality whether in a peripheral or central sense. Reason moves, it were, in a vertical axis that is both transcendental and immanent at one and the same time and which is also fully subjective in status.
We have only to think of the Pythagorean theorem as an example. The central truth of this theorem could be established in two different ways well known in the classroom. Those of the lower grades arrive at the truth by a method resembling that of experimental trial-and-error. It would consist of making drawings of right-angle triangles on paper and then constructing squares on each side, on any number of such triangles of varying sized and dimensions. These squares could be cut out according to certain plans. This practical method can prove that the squares of the sides are together equal in a area to the square on the hypotenuse. There is also the more usual method of proof that school children learn at a later stage when their esprit de finesse is more fully developed. This latter proof is through graded acceptance of axioms, postulates, propositions, theorems, riders and lemmas.
Each lends certitude to the other in a graded hierarchy of descending truth-values. By manipulating them in a certain way the teacher is able to "prove" on the blackboard the same truth that the children in the lower grades arrived at through their esprit géometrique as Pascal would have called it.
There are not two verities involved here. The central truth is neither pure nor practical, but a resultant of both. Mathematics and logic are processes of thinking. They are independent of things physical or objective in the actual sense, and may thus be imagined as approaching each other on two poles of the vertical axis, having at one and the same time both an immanent and transcendent epistemological status. Two proofs thus meet in one neutral certitude at the core of consciousness. This certitude, having a subjective transcendental-cum-immanent order of its own, properly belongs to a normative Science of the Absolute.
In the familiar parlance of Vedanta Philosophy this way of reasoning is referred to as the one that abolishes triputi (tribasic prejudice in thought) for purposes of proper absolutist speculation. Horizontally viewed in the context of actualities or corresponding virtualities, as they refer perceptually to the senses, this is necessarily divided tri-basically into subject, object and central truth-value. This splitting of awareness into three disjunct components is not favourable to unitive or integrated certitude. We have to be able to take a verticalized view of this same tribasic situation.
As in the example of the Pythagorean theorem, the immanent aspect of this tribasic situation is represented by the schoolchildren dealing with actual triangles and squares cut out on paper. The transcendental aspect corresponds to a more generalized and abstracted version of the horizontal tribasic situation.
The proof of the Pythagorean theorem results when both the immanent and transcendental approaches cancel themselves out into a central certitude which is truly absolutist and neutral. This neutral seat at the core of consciousness is the correct epistemological source of all scientific or metaphysical certitude.
The essence of the dialectical method can be seen here to be incorporated naturally into a kind of speculative reasoning, both experimental and axiomatic at the same time. The self-consciousness of man understood under the notion of the Absolute is what finally gives certitude to all or any miscellaneous certitude we seek in life. Syllogistic reasoning is only a lukewarm or feeble version of the same certitude characteristic of reasoning. Many other forms of eristic or sophistic reasoning are no better. Trial-and-error experimentation can be considered only ratiocination of the lowest order, possessed even by animals. The high sounding inductivo-hypothetical method is only a form of glorified guesswork. The method of sampling based on statistical averages and probabilities yields a weaker form of certitude still. No probability can be established except where possibility has first been established. All possibilities which can be proved by even one unique case of success instead of depending on large statistical averages, are basically nearer to the context of the Absolute than to the pluralistic world of multiple interests in life.
Significant human value-certitudes necessarily reside at the core of human consciousness itself and belong to the context of dialectic as properly understood in a science of the Absolute.
14. FURTHER LIGHT ON THE SCOPE AND LIMITATIONS OF THIS SCIENCE
We have indicated so far the global, integrated or unitive nature of our subject matter; the approach being from the physical and metaphysical aspects of the subject-matter and object-matter of science treated together. This is done in a neutral manner without prejudice to either of these disciplines. Having indicated how dialectical methodology properly belongs to the content of the Science of the Absolute, there remain some structural outlines to be clarified, as also some logical parameters derived from thermodynamic or cybernetic disciplines.
15. CONTRIBUTIONS OF VEDANTA EPISTEMOLOGY
We have just said that the tribasic prejudice natural to man has first to be neutralized if a unitive verticalized version of total truth or value is to emerge. Let us again rely on Vedanta tradition and refer to the three aspects familiarly understood as sat, cit, and ananda into which the notion of a central global Absolute can be referred for purposes of critical analysis and easy communicability.
Anything that deserves the attention of man must fulfil the following three basic requirements: it must first respond to the question whether it exists; it must respond to the question whether it remains true even when subjected to logical scrutiny: and thirdly, whether it has any value-significance to man.
In Vedanta each fact, reality, or truth is either existent, subsistent or has value. Existence corresponds to the Sanskrit term sat (also called asti: exists), and is ontological in its philosophical status.
Subsistence, which determines something that subsists or is substantial and looms into consciousness even after reason has been directed to it, is referred to as cit, of which the act of entering consciousness is called bhati (looms). The axiological aspect is also added on top of existence and subsistence and recognized by the term ananda (value factor), also called priya (dear). The totality of the Absolute as it interests man, is comprised within these three categories of existence-subsistence-value corresponding respectively to asti-bhati-priya. (26)
It should not however be imagined that these categories stand apart disjunctly. Each one is meant to neutralize or modify the asymmetry implied in the other, so as to fuse the three categories into one homogeneous content belonging to the same golden streak of a real and central logical or rational truth-value. Vedantic tradition also indicates other lines which any integrated Science of the future must follow. The departmentalization of cosmology, psychology and theology is not favourable in bringing to light any unified Science. It is therefore always tacitly understood in Vedantic tradition that the adhibhautika (what refers to the elements, i.e. cosmological), adhyatmika (what refers to the self, i.e. psychological), and adhidaivika (what refers to the gods, i.e. theological and therefore axiological), should all be comprised within the scope of any complete philosophy.
The cosmological, psychological and theological have always to go hand in hand with the notion of the Absolute as the unifying reference. Besides these two Vedantic conventions there is also a third to keep in mind. This last convention refers to the two broad divisions of the situation with which the contemplative is most directly concerned.
Nature, into which all men are born, when treated as a global datum, has two aspects. One can be characterized objectively as "made for man" and the other, its reciprocal opposite, refers subjectively to "man as its enjoyer". These two are distinguished respectively by the technical term often employed in Vedantic literature: Viz. bhogya (something to be enjoyed or appreciated as having value-significance), and its natural and inevitable dialectical counterpart bhokta (the enjoyer) which is the subject represented in the Self. Fichte also correctly treated the Self and the non-Self as bilateral counterparts in his philosophy. Thus Nature corresponds horizontally to the Natura Naturata and vertically to the Natura Naturans of Spinoza. Among modern scientists of high standing it is Erwin Schrodinger who recognized for the first time how conveniently suitable the Vedantic way of thinking was for paving the way for the future integration and ordering of the epistemology and methodology of a Unified Science. We shall return to take advantage of his remarks at a later stage. For the present the three integrating items we have borrowed from Vedanta must suffice to give us a general idea of the scope and normal delimitations of our subject.
We have to first remember that triputi (tribasic prejudice) is to be abolished; secondly, that sat, cit and ananda are to be treated as triple categories neutralizing each other; thirdly, that cosmology, psychology, and theology should always be kept hand in hand in our discussion; and finally, that the vertico-horizontal correlation is always to be kept intact between the Self and the non-Self, as enjoyer and what is to be enjoyed (bhokta and bhogya). When this is remembered, we shall have fulfilled some of the more important and fundamental prerequisites of an integrated Science of the Absolute.
16. THE SCIENTIFIC CERTITUDE CLAIMED IN THIS WORK
All certitude resides, as we have already explained, at the core of absolute consciousness. On final analysis the Absolute proves itself from both sides of the total knowledge-situation. It was Eddington who was responsible for the pleasantry : "Proof is an idol before whom the pure mathematician tortures himself." (27) Wittgenstein, on the other hand, has become famous for saying that all propositions prove themselves. He states the following axiom in his famous Tractatus:
"Every proposition must already have a sense: it cannot be given a sense by affirmation. Indeed its sense is just what is affirmed. And the same applies to negation, etc." (28)
And further on he states (in 6.125):
"It is always possible to construe logic in such a way that every proposition is its own proof." (29)
We have also the popular saying, "The proof of the pudding is in the eating thereof. " This is judging proof by effects.
Absolute proof can be judged by the correctness of its starting postulates or by its experimental conditions, as when an experiment is correctly arranged and made to work in the laboratory. "It works," is a sufficiently valid proof in the simple mechanistic world. We have previously examined how the Pythagorean theorem could be proved from two ends of the total knowledge-situation. How causes meet correct end-results, giving validity both ways, is the type of proof to be kept in mind when we think of this present work. Neither the laboratory nor the observatory is all-important. Nor do we completely rely on the body of general ideas, often haphazardly put together in seminaries and scholastic centres of learning. We have to take account of both sides from a normalized central position, where the visibles and the calculables come together and confirm each other. It is therefore in the very centre or middle term that the greatest scientific certitude is to be sought; neither in its major nor minor, positive or negative ones. As we depart from this central position we come to unilateral domains of certitude, tending to reach the existential bottom of the vertical axis, or the vague axiological pole of reality at the top of the vertical axis.
These two partial certitudes that reside experimentally or axiomatically at the two poles of the pure and almost mathematical knowledge-situation tend to tally by the efforts made by the true contemplative. When the tallying is perfect normalization and renormalization yield the central, normative notion of the Absolute.
Modern science consists of findings which are capable of being expressed in the form of equations. Einstein, Planck or Schrodinger, each has his famous equations expressed not only in algebraic symbols, but also incorporated into their structural counterparts which are geometrical in status. Equations in analytical geometry answer to graphs and vice versa, and they may be said to prove each other giving a fully scientific character to the certitude involved. Post-Hilbertian geometry is now an independent self-sufficient discipline, whose theories and actual objects come together, yielding high scientific certitude in the field of mathematics.
In the present case of the normative notion of the Absolute, its beauty, power and fecundity besides practical applicability to the whole domain of knowledge should be taken as a sort of proof by end-result". The starting premises of our work are also unquestionable, because the direct evidence of the senses is not denied its legitimate right to influence or guide our thoughts throughout the range of this Science.
Pratyaksha, a Vedantic term which refers to the empirical evidence on which the positive sciences normally rest, is given its due place in the methodology of the Vedanta. Ontology, in Vedanta, refers to the very first item of the triple categories that finally compose the Absolute, which have been referred to collectively as sat-cit-ananda (existence-subsistence-value). Vedanta is therefore not an "idealistic" philosophy as some authorities tend to think but one that is a normalized version of truth arrived at from both the ends of existence and value.
At the other pole of the knowledge-situation, Vedanta fully recognizes what it calls sabda-pramana, the validity of the Word. This refers to the a priori or the axiomatic in the domain of pure names where each proposition can fully prove itself without any consideration of contradiction entering into it. At the very core is to be located the normalized neutral certitude, which is no less scientific than the other two and on both of which it depends. This verity is not unknown to some modern thinkers. Bergson strikingly refers to these "two efforts of opposite direction" as follows:
"Coinciding with this matter, adopting the same rhythm and the same movement, might not consciousness, by two efforts of opposite direction, raising itself and lowering itself by turns, become able to grasp from within, and no longer perceive only from without, the two forms of reality, body and mind? Would not this twofold effort make us, as far as that is possible, re-live the absolute?" (30)
Even in ordinary life if one should call a carpenter and ask him to make three or four yardsticks or footrulers, the correctness of what the carpenter produces could be questioned, in spite of the minutest efforts to make them exact. The questioning man who wants to accept them after applying the right tests would have to lay them one over the other to see if the edges tally, and then also verify the lengths with the standard yardstick kept, say in the British Museum. The second test is based on something a priori and arbitrarily fixed.
The truth of such a standard is accepted nominalistically. It is not questioned and belongs to the world where something can prove itself. After making one yardstick with the help of the standard bar, the carpenter duplicates or triplicates it, employing the Euclidean axiom, "things which are equal to the same thing are also equal to one another." (31) Here again the carpenter abandons the visible test and accepts unconsciously the calculable or intelligible. The man who is to pay for them first tests them by piling them one on the top of the other, passing his fingers on both ends of the sticks to see if they are all the same. If he finds even a hairbreadth of a discrepancy he would (or should) reject them, and ask the carpenter to standardize or normalize them more correctly.
Thus even here in such a simple operation of everyday applied science we find both the observables and calculables entering into interplay yielding the desired result, and having a correct scientific significance in daily life. When this is so in such simple cases, it is not necessary for us to give other detailed examples. There could be great disparity between the experimental and calculable aspects of certitude which enter into the formulation of a general law such as Newton's theory of gravitation. Textbooks tell us that he did not get the initial suggestion from any experiment conducted in the laboratory, but instead happened to see an apple fall from a tree.
This was enough to start him on a train of thought whereby he traveled through the astronomical calculations of Kepler and others before him. Newton, by this strong common sense or intuition was bold enough to formulate a theory that has not ceded its position as a central theory even in our post-Einsteinian world, referring to the whole universe anywhere and at any time. The experimental portion properly belonging to this bold theorization happens to be minimal, yet the beauty, fecundity and force of Newton's vision remains and uniquely dominates the total scientific world, still commanding our admiration.
Another striking innovation in the world of modern thought is the discovery of the coordinates by Descartes, which are being used now in almost every department of precise thinking. A nurse in a hospital, a pilot of a ship heading towards a port, makers of maps and directories, and even those tabulating a simple thing like bus fares, all use the Cartesian coordinates. They are also used, ever-increasingly in the domain of verification of abstract equations, such as those of Schrodinger for his suggested field theory. These coordinates of Descartes constitute a powerful instrument of scientific research depending on itself for its validity. The credit of this epoch-making discovery goes to the great philosopher. Likewise, the scientific validity of the present work which is not concerned merely with one department of science, nor with one way of speculation to the exclusion of all others, looks primarily for its certitude within itself.
Its starting assumptions and end-results have to tally in such a way as to confirm each other. It is the common structure underlying both the visible and the intelligible aspects of reality when treated together, that is our final normative reference. As Whittaker pointed out, the a priori framework of the universe and its material aspect have to lend certitude to each other.
Distinguishing them in clear terms he writes:
"We stand in awe before the thought that the intellectual framework of nature is prior to nature herself - that it existed before the material universe began its history - that the cosmos revealed to us by science is only one fragment in the plan of the eternal." (32)
Such is the central seat of the norm for certitude with which we are concerned. Whittaker himself elsewhere speaks of normalization and re-normalization for certitude. If we are able to consistently reveal the same structural outlines of logical parameters throughout the range of the various disciplines involved in our subject, the requirements claimed for such a Science of Sciences will be fulfilled to the maximum measure.
17. NORMALIZATION AND NEUTRALIZATION OF SCIENTIFIC THINKING
Facts, truths or local events as reported in newspapers and periodicals have only an incidental and non-generalized character. Scientific or philosophic thought consists of not allowing any prejudice or partiality to vitiate eternal and universal verity, either as a Truth of existence, subsistence or value. Scientific thought and philosophical speculation become all the more dignified when they have a correct and global symmetry of structure. Science is only interested in universal values. Schrodinger points out the difference between the correctly philosophical and the non-philosophical attitudes as follows:
"The unphilosophical and philosophical attitudes can be very sharply distinguished (with scarcely any intermediate forms) by the fact that the first accepts everything that happens as regards its general form, and finds occasion for surprise only in that special content by which something that happens here today differs from what happened here yesterday; whereas for the second, it is precisely the common features of all experience, such as characterise everything we encounter, which are the primary and most profound occasion for astonishment; indeed, one might almost say that it is the fact that anything is experienced and encountered at all." (33)
All partialities have to be rubbed off. Even prejudices such as big and small, part or whole, one or many, whether belonging to the context of being or becoming; all have to be rounded off to bring fact truth or value under the aegis of the normative notion of the Absolute. If we say, for example, as Protagoras said, that, "Man is the measure of all things," we have to examine man as placed in his total environment in the universe. He has to be placed in the complete context to which he properly belongs.
Instead of man we can think, as in the Socratic context, of "Know thyself," pertaining to human consciousness. Here again consciousness has to be understood with all its implications of being or becoming. It can only be divided into bits sub species aeternitatis, if we are to correctly understand Spinoza's notion of substance. Its natura naturans and natura naturata have to be considered as belonging together. If we think of Liebniz and his monad, the plurality of monads should not be considered prejudicial to the understanding of the overall relation of the monas monadum or the Monad of Monads, to the structure to which each monad is meant to conform. Liebniz writes about the monad as follows:
"1. The Monad of which we speak here, is nothing but a simple substance, which enters into compounds. By 'simple' is meant without parts.
2. And there must be simple substance, since there are compounds; for a compound is nothing but a collection or aggregation of simple things.
3. Now where there are no parts, there can be neither extension nor form (figure) nor divisibility. These Monads are the real atoms of nature and, in a word, the elements of things." (34)
In the Upanishads we have varying instances of items of simple existence, subsistence or value taken and treated as proper to the context of a normative notion. Abstraction and generalization have to go hand in hand without losing their way in the bypaths giving place to distortions or exaggerations of facts or events. We have seen how Plato glorifies without distortion or exaggeration such notions as Truth and Beauty, thus correctly placing them in the world of high values where they properly belong.
Any "ism" such as polytheism or pantheism can be justified if such notions are fitted into, and understood in, the overall context of the structure of the Absolute, without any unilateral lack of proportion or harmony with other items belonging to the same group or family of ideas. The task of normalization and neutralization in any integrated or unified Science has to respect all such important pre-requisites.
In his "An Introduction to Metaphysics" (35), Bergson has enumerated some other items belonging properly to the absolutist approach. Modern phenomenology has also adopted a normalized method of scientific speculation which respects such a normative approach, although it still fights shy of the a priori approach and other such classical notions, even when they are harmless. (See page 9 and our reference to Husserl.) Among modern scientists it is once again Schrodinger who is able to point out this necessity of normalization for future scientific thinking.
As an example of neutralized thinking between life and matter in the biological context, it is interesting to read his plea for a kind of neutral and monistic approach to the consciousness in which animals such as the fly hydrafusca may be said to live. He closely considers the phenomenon of regeneration in this species of living beings, and he is able to prove, with the help of other experts in biology, that the animal lives in an indivisible unit of consciousness of its own.
Matter and mind could similarly be thought of as belonging together in the neutral zone or stratum of absolute consciousness. Such a view is natural to Vedanta. Even outside Vedanta great thinkers like William James have referred to the same factor as neutral monism. All variations of the visible world can be reduced to generalizations or abstractions having a schematic status, while all names and classes belonging to the world of concepts can be fitted together into one unitive category in generalized abstract terms. When the schema and the nominalistic abstraction lend truth-value to each other, correct scientific speculation becomes possible even in the context of the Absolute. Schrodinger gives another picturesque example of this Vedantic way of normalization. It is interesting for us to quote him here at some length, both because it would serve as a model for scientific thinking, and more especially because it comes from a scientist fully alive to the requirements of a revised way in scientific thought. What is more, he cannot be charged with any traditional prejudice in favour of the Vedantic method which he so highly commends.
"Suppose you are sitting on a bench beside a path in high mountain country .... and facing you, soaring up from the depths of the valley, is the mighty, glacier-tipped peak, its smooth snowfields and hard-edged rock-faces touched at this moment with soft rose-colour by the last rays of the departing sun, all marvelously sharp against the clear, pale, transparent blue of the sky.
"According to our usual way of looking at it, everything that you are seeing has, apart from small changes, been there for thousands of years before you. After a while - not long - you will no longer exist, and the woods and rocks and sky will continue, unchanged, for thousands of years after you. What is it that has called you so suddenly out of nothingness to enjoy for a brief while a spectacle which remains quite indifferent to you? The conditions for your existence are almost as old as the rocks. For thousands of years men have striven and suffered and begotten and women have brought forth in pain. A hundred years ago, perhaps, another man sat on this spot; like you he gazed with awe and yearning in his heart at the dying light on the glaciers. Like you he was begotten of man and born of woman. He felt pain and brief joy as you do. Was he someone else? Was it not you yourself? What is this Self of yours? What was the necessary condition for making the thing conceived this time into you, just you and not someone else? What clearly intelligible scientific meaning can this 'someone else' really have? If she who is now your mother had cohabited with someone else and had a son by him, and your father had done likewise, would you have come to be? Or were you living in them, and in your father's father .... thousands of years ago? And even if this is so, why are you not your brother, why is your brother not you, why are you not one of your distant cousins? What justifies you in obstinately discovering this difference, the difference between you and someone else, when objectively what is there is the same?
Looking and thinking in that manner you may suddenly come to see, in a flash, the profound rightness of the basic conviction in Vedanta: it is not possible that this unity of knowledge, feeling and choice which you call your own should have sprung into being from nothingness at a given moment not so long ago; rather this knowledge, feeling and choice are essentially eternal and unchangeable and numerically one in all men, nay in all sensitive beings." (36)
The Vedantic way of approach to science or even to metaphysics is thus correctly in accord with what modern scientists like Schrodinger think on this subject.
18. THE GAP BETWEEN EXPERIMENTAL AND A PRIORI THINKING
In the mind of even some of the most advanced modern scientific thinkers there seems to persist a strange prejudice against giving an equality of status to both a priori and a posteriori processes of thinking. These terms are themselves sometimes even considered outmoded, at least to the post-Voltairian western mind, and flavouring of the Dark Ages and the horrors associated with it. Prejudices die hard, and orthodoxies and heterodoxies are like a pendulum swinging from one extreme to the other. Even such an advanced thinker as Einstein, who had the boldest of dreams about establishing a Unified Field Theory, remained to his last days a staunch adherent of experimental evidence as against the a priori. This is evident in one of his later writings, entitled "Space, Ether and the Field in Physics", where he puts forward his finalized theoretical version in respect of his noble dream.
This prejudice in favour of the observables as against the calculables, comes into evidence very distressingly for us here. Referring to the change of attitude in the method of science, of which Einstein was fully conscious, and in spite of the rival claims of the deductive as against inductive methods, he does not seem to be prepared to shed his prejudice in favour of observed facts. Nonetheless some of his own followers like Eddington have accomplished a breakthrough in this matter, standing for what we have previously discussed above as normalization.
The idea of taking a neutral position between rival claims of observation and the a priori method has not established itself fully in the thought of scientific thinkers. Einstein admits the claims of deduction as against induction as follows:
"The predominantly inductive methods appropriate to the youth of science are giving place to tentative deduction. Such a theoretical structure needs to be very thoroughly elaborated before it can lead to conclusions which can be compared with experience." (37)
It was really after the posthumous publication of the Fundamental Theory of Eddington that Whittaker and Milne began to think in terms of normalization and renormalization of the experimental with a priori calculations. This hesitation in giving axiomatic thinking its due place in the total scheme of normative absolutist thinking, so desirable for a Unified Science, has been one of the main impediments for the progress of thought in the direction of fully meeting the imperative demands of a Science of the Absolute.
In spite of the difficulty however, even as early as in the time of Constantine the Great, his nephew, the Emperor Julian, was able to write as follows:
"Reflect, therefore, whether self-knowledge does not control every science and every art, and moreover whether it does not include the knowledge of universals. For to know things divine through the divine part in us, and mortal things too through the part of us that is mortal - this the oracle declared to be the duty of the living because individually he is mortal, but regarded as a whole he is immortal." (38)
Bridging the gap between the experimental and axiomatic is the one task staring the modern scientist in the face. This task requires much imagination, intuition and even a great amount of hard thinking. One has to make the mind leap forward from the visibles to the intelligibles, and at the same time back from the opposite pole, employing a descending dialectical approach. Induction and deduction have to interlace correctly and yield new ontological, logical or axiological parameters for thought. Such a task demands the best powers of the speculator and the most penetrating powers of the mind of the experimentalist. In tentatively formulating the theoretical considerations for his Unified Field Theory, Einstein was fully conscious of the difficulties present in such a task. In a striking passage, written after 1950 a few years before his death, we hear him pleading for much latitude to be given to anyone who would propose a theory bridging the gap between the experimental and axiomatic aspects of thought. In continuation of what we have already cited above, we read as follows:
"But it (deduction) cannot pronounce sentence until the wide chasm separating the axioms from their verifiable consequences has been bridged by much intense, hard thinking. The theorist has to set about this Herculean task in the clear consciousness that his efforts may only be destined to deal the death blow to his theory. The theorist who undertakes such a labour should not be carped at as "fanciful"; on the contrary, he should be encouraged to give free rein to his fancy, for there is no other way to the goal. His is no idle day-dreaming, but a search for the logically simplest possibilities and their consequences. This plea was needed in order to make the hearer or reader more ready to follow the ensuing train of ideas with attention; it is the line of thought which has led from the special to the general theory of relativity and thence to its latest offshoot, the unitary field theory." (39)
What Einstein pleads for in the above quotation, if it is to be conceded to him and his fellow scientists, must also be equally applicable to us. The task is no doubt very difficult, but if we first shed the die-hard prejudices in favour of induction the task will at once change its complexion and become favourable and even easy to accomplish.
At the present day there are new structural outlines and logical parameters coming into evidence in scientific thinking. Some belong to the context of biology, while others to electromagnetism or thermodynamics.
This structural outline always implies two poles, one positive and the other negative, with a reciprocity between them. In biology this reciprocity is referred to under the names of ambivalence or dichotomy. This double aspect is seen between the diastole and systole in the functioning of the heart, where this ambivalent dichotomy is present as a normal feature. The growth and division of organisms also present the same ambivalent dichotomy, involving a reciprocal compensation between them. In the osmotic interchange of fluids across living membranes, we have a double process of exosmosis and endosmosis. We can also imagine this as taking place along a subtle functional parameter. Thermodynamic equilibrium, with its notion of entropy and negentropy suggests a vertical line in which compensation can be thought of as ascending or descending to or from a zero point.
The parameter proper to information as understood in cybernetics is also very intriguing and interesting in the same context. Logistics, semantics, and linguistics, too, have their similar subtle inner relational principles, revealing the element of a hyphen (trait d'union), linking reciprocally the antinomies between the physical and metaphysical, the experimental and axiomatic, and the a priori and a posteriori.
We shall review all these in a later section. What we wish to underline here is the still persistent die-hard conservatisms and orthodoxies lingering within scientific thought. This is perhaps the one great impediment in the matter of arriving at a unified normative Science.
The very name "Absolute" as we have said earlier, is anathema to most modern thinkers.
19. EXPERIENCE AND EXPERIMENT HAVE TO INTERPENETRATE TO REVEAL THE ABSOLUTE
Bergson is a unique exception among modern philosophers in that he finds the notion of the Absolute very appealing. In the nearly 1500 pages of the "Collected Works", ("Oeuvres") (40) in French, he seems at least implicitly, to have kept this in his mind throughout.
In many places in his writings he opens the door of the secret compartment of this absolutist vision to his readers, and after having given them only a glimpse of what the chamber contains, closes it once again. He is careful not to leave it too wide open lest too much exposure of the Absolute is given to the vulgar view of man, especially modern man; which would have spoilt the case for his philosophy as a whole in which he desired to maintain a fully scientific character.
Bergson has uniformly maintained in his philosophy the intermediate position between what is discovered by the experiments of science and what is attained through the immediate intuitional inner experience given to all living beings. If he adopts a brand of evolution of his own called "creative evolution" it is in order not to part company with the pragmatists and scientific thinkers of his time.
He has been generously included as belonging, in an extended context, to the school of pragmatists of whom Charles S. Pierce and William James were the leaders.
It is legitimate, according to this school of thought, to call him an instrumentalist in spite of the fact that the intuition found in Bergson's philosophy cannot strictly be included within the scope of pragmatic thinking.
According to Bergson, physics and metaphysics are meant to belong together as one and the same discipline where observation, logic and intuitive reasoning interpenetrate. It is as in a game of cricket, where the bowling and batting teams occupy opposite sides of the field and alternately move from one side to the other. Metaphysics and physics are to be considered as capable of being played together on one field.
Bergson was avowedly an intuitionalist but talked of the pure creative movement of a visible natural evolution of life. Here he was bold enough to modify and correct all previous philosophers. He considered them to be vitiated in various degrees by static, mechanistic or over-conceptualized abstractions, tending to be only mathematical and estranged in various degrees from the living breath of reality. We have already devoted a complete study, entitled "The Search for a Norm in Western Thought" (41) to showing the central neutral notions tacitly or overtly kept in mind by various western philosophers. In that study, we began with the English Empiricists, passing through the range of the brilliant rationalist group from Descartes to Kant, and terminating with the group of German idealists who rose to great heights of subtle philosophical speculation.
The norm in the mind of the modern empiricist is too implicitly taken for granted and covered by vague blanket expressions like "human understanding." With the Rationalists, of whom Descartes may be said to be the father, both algebraic and geometrical thinking began to be combined, starting a new tradition altogether. The Cartesian correlates for the first time gave a schematic status to the nominalistic thinking brought into vogue by the scholastics of the period. Such schematization, once recognized, led Spinoza in his turn to think in terms of a mesh of small squares with which he proposed first to analyze the notion of the Absolute. Leibniz was also one of the dreamers of a universal mathematics basing itself on innate universal characteristics along with a technique of arriving at complex concepts by combining a relatively few simple ones taken as primitive. This technique he called ars combinatoria. With this he built up perhaps the most ambitious and elaborate picture in respect of the content of reality, as found in his Monadology.
Cartesian structuralism and the newly discovered principles underlying the differential, integral and infinitesimal calculi were all brought to bear on his monadological picture of the universe. Finally Kant gave this mathematical and picturesque tendency a correct epistemological status at the core of reality.
In his notion of schematismus, Kant was careful to point out that the categories of abstract thought, as they combined themselves with visible aspects of a representation of reality, formed together the double-sided schematismus which he was able to elaborate in his writings only to a limited extent, as we can see from the following from Kant:
"Schematism is an intermediary function between sensibility and understanding, which on the one side unifies the sensible in order to make it understandable through concepts and on the other gives to the concept a sensible figuration (for example the scheme of causality is succession). The schema is thus homogeneous on the one side to the concept, and on the other to the sensible: it makes possible the inclusive assumption of the sensible under concepts." (42)
Finally came Bergson's own way of sweeping over, as it were, the whole range of philosophy, wherein the breezes of intuitive thinking gave, as Wilson Carr remarked, "fresh life to the dry leaves or bones which philosophy consisted of before him." If we look upon his philosophy with some favour it is because of the fact that, for the first time in the history of modern thought, science and metaphysics began to touch and even complement each other as disciplines interpenetrating as it were into a central unity from two opposite poles, thus making it possible for us to have a glimpse, at least, of the abstract notion of the Absolute, treated together with its living contents, without being merely axiomatic or factual.
In many parts of his work, Bergson has had occasion to discuss the rival epistemological claims between the notions of time and space.
Pure duration, which Descartes was able to equate with God, enters the domain of the inner experience of each person as it is given to him in his personal conscious intuition. Space, on the other hand, tends to be a horizontalized cross section of the content of time, which Bergson always compared to a block or pile of a series of successive stills as contained in the cinematographic apparatus. (43) According to the terminology consistently developed by us in all our previous studies, it is now permissible to refer more simply to these aspects as vertical and horizontal correlates of the Cartesian coordinate system.
These two co-ordinates interpenetrate, articulate or participate unitively at the core of absolute self-consciousness on a homogeneous, neutral and transparent ground transcending paradoxical elements.
Bergsonian metaphysics insists on this interiorized relation between the subject and object, viewing it as an eternal flux of creative becoming. If we treat being and becoming as prejudices natural to human beings, we can think of the possibility of abolishing both these factors and then fully attaining the Absolute. Except for this last stand which we take, we accept with complete confidence the metaphysics of Bergson. What interests us now is the single feature that distinguishes the Bergsonian way of speculation which, instead of treating physics and metaphysics as distinctive or disjunct disciplines, tends to treat them together without any inner conflict or outer contradiction. The case for schematism is itself restated in revised and more dynamic terms by Bergson in his schema moteur.
His heritage is the same Cartesian one shared with others like Spinoza and Leibnitz. In this sense Bergson can be named as a pioneer in scientific philosophizing.
The same heritage to which we have just now referred has also influenced Eddington and Milne, who may be described as philosophers of science, rather than scientific philosophers. Eddington puts forward three characteristics of what he calls his philosophy, which he takes care to mention as coming from the general heritage of philosophy and not altogether his own. These three features are subjectivism, selectionism and structuralism. By subjectivism he wants to give primacy to concepts rather than objects of reality. By selectionism he means the same as when any other philosopher enumerates his main categories. By structuralism he refers to the form or frame of reference to which all thought or reality has to refer and conform. Thus a two-sided approach to normative absolutist thinking is now almost an accomplished fact even in Western thought. It is now in vogue to speak of a field theory which evidently presupposes something visible as in a magnetic field of force revealed by iron filings scattered over a piece of paper laid over a magnet. This is fashionable in inertial and gravitational field theories. The latter perhaps refers more to the universal verticalized content than the former, which is limited only to visible facts. The claims of structuralists are only now being consistently established. M.A. Tonnelat and P. Destouches-Fevrier, working under Louis de Broglie in the University of Paris, must be credited with efforts to make structuralism fully valid in the domain of modern science. (44)
Some of their works are still considered a little in advance of their time and the full approbation of their views by elder scientists is being awaited. Hilbertian mathematics has also given a strong impetus to structural ways of thinking, and it can be predicted that structuralism in the near future will be fully recognized as the factor giving unity and validity of reference to many widely different disciplines.
Even before such a vogue in favour of structuralism became evident in the 1950's, it is remarkable to find Bergson fully and consciously anticipating this development. The following words are quoted from Bergson at length, because of their importance to us in this work:
"It is impossible to consider the mechanism of our intelligence, as well as the progress of our science, without arriving at the conclusion that between intelligence and matter there is in effect a symmetry, concordance and correspondence. On the one hand, in the eyes of the savant, matter resolves itself more and more into mathematical relations, and, on the other hand, the essential faculties of our intelligence do not function with an absolute precision except when they are applied to geometry. Doubtless, mathematical science could not have taken, at its origin, the form that the Greeks had given to it. Doubtless also, it must force itself, whatever form might be adopted, to the use of artificial signs.
But previous to this formulated mathematics, which covers within itself a great amount of convention, there is another, which is virtual or implicit and natural to the spirit of man. If the necessity for operating on certain signs makes it difficult for many of us to arrive at mathematics, on the contrary, as soon as the obstacle has been surmounted, the spirit moves in this domain with an ease which it can find nowhere else. The evidence here is immediate and theoretically instantaneous. The effort to understand most often exists in fact but not in principle: in any other department of study, on the contrary, in order to understand, an effort of maturation of thought must be made, which remains in some way adhering to the result, essentially filling duration, and which would not lend itself to be understood as instantaneous even theoretically. Briefly, we could believe in a gap between matter and intelligence if we could consider matter as nothing other than the superficial impressions made on our senses, and if we should leave to our intelligence the fluid and vague form which it has in its everyday operations. But if we should bring intelligence to its precise contours, and when we search more profoundly and sufficiently our sensible impressions in such a way that matter begins to give up the interior of its structure to us, we find that the articulations of intelligence come to apply themselves exactly on those of matter. We do not see, therefore, why the science of matter should not attain an absolute. It attributes to itself instinctively this significance and all natural belief should be considered to be true, and all appearance as reality, as long as one has not established its illusory character. On those who declare our science to be relative, as well as on those who claim that our knowledge deforms or constructs its object, devolves the charge of proving it. And they would not know how to fulfill this obligation because the doctrine of relativity of science does not know where to find a place for itself when science and metaphysics are on their true ground; that on which we replace them here. (45)
The above passage not only refers to structuralism but also to other aspects of a unified Science of the Absolute.
20. "WOULD NOT THIS TWO-FOLD EFFORT MAKE US RELIVE THE ABSOLUTE"
Elsewhere in a striking quotation Bergson goes into the modus operandi of the structural correspondence between mind and matter. It is worth while referring to it:
"Coinciding with this matter, adopting the same rhythm and the same movement, might not consciousness, by two efforts of opposite direction, raising itself and lowering itself by turns, become able to grasp from within, and no longer perceive only from without, the two forms of reality, body and mind? Would not this twofold effort make us, as far as that is possible, re-live the absolute?" (46)
These remarks could not come from a modern European philosopher unless he was nourished or influenced by some deep-seated tradition in speculative thinking inherited from either the Hellenic or Hebraic backgrounds. We might even suspect, with little justification in the present case, that he might also have been influenced by Indian thought. Bergson's words imply rare kinds of presuppositions about the nature of the spirit of man, and how it could operate so as to make the attainment of the Absolute come within our reach. We know from other evidence that he leaned largely on pre-Socratic philosophers.
The way Parmenides and Zeno resolved paradoxes pertaining to the One and the Many, and those in the context of pure motion, were ideas very dear to him. (47)
It is not therefore far fetched to suppose that Bergsonian speculation was largely nourished on the pre-Socratic school of thought which was fully scientific in its outlook. Even a modern logical positivist like Bertrand Russell, who is fully insistent on the matter of conformity to scientific thinking, in spite of his many reservations about Heraclitus, still refers to him with approval and even considers him great. After praising Heraclitus as a great philosopher, Russell continues: "From the few fragments that remain, it is not easy to discover how he arrived at his opinions, but there are some sayings that strongly suggest scientific observation as the source" (48)
Heraclitus does not represent anything other than what his natural pre-Socratic, Eleatic and hylozoist philosophical tradition stood for. To explain how Bergson, at the very heart of modernism, could make such bold claims as "re-living the Absolute" can even become thinkable only when we hearken back to this ancient group of philosophers living among the scattered and far flung islands away from Athens. To be able to understand that Bergson's many indirect references to the Absolute are not freak expressions that suddenly come into view in his philosophy this pre-Socratic heritage must be kept in mind.
The entire attitude of the Ionian pre-Socratic philosophers can be contrasted with what came to be considered philosophy after Plato. With Plato ideas were primary and metaphysics soared freely, ascending through speculation or else descending from the world of ideas or intelligible hypostatic values. On the other hand, the hylozoism of the Eleatics erred, if at all, in the opposite direction. They believed first in the reality of the elementals although they were also able to go in and through the elements to higher abstract notions such as that of the Nous of Anaxagoras. Unlike the Logos brought into full view many years later by Philo the Jew (30 BC - 50 AD), the Nous had a rival epistemological status, being derived from the existential aspect of reality rather than from the highly abstract world of Platonic Values. Hylozoists, beginning with Thales (6th c. BC), were down-to-earth from their starting point and first gave importance to water as a fluid principle representing reality. Anaximander (6th c. BC), who was a follower of Thales, improved on this, discarding hylozoism to some extent while thinking of an infinite substance which he identified with the material cause of the universe.
It is said of him:
"The material cause and first element of things was the Infinite, he (i.e. Anaximander) being the first to introduce this name of the material cause. He says it is neither water nor any other of the so-called elements, but a substance different from them which is infinite, from which arise all the heavens and the worlds within them." (49)
Anaxagoras, who lived later than Anaximander (c.430 BC), raised the status of this Infinite Substance into something "thin and pure" which he called the Nous. He explained:
"In everything there is a portion of everything except Nous, and there are some things in which there is Nous also.
Nous is infinite and self-ruled, and is mixed with nothing, but is alone, itself by itself ....
For it (i.e. Nous) is the thinnest of all things and the purest, and it has all knowledge about everything and the greatest strength; and Nous has power over all things, both greater and smaller, that have life. And Nous had power over the whole revolution, so that it began to revolve in the beginning." (50)
Empedocles (490-430 BC) went still further in analyzing the subtle, inner, four-pointed mechanism which in physics and metaphysics later became interchangeable processes of thinking.
"There is a double becoming of perishable things and a double passing away." (51)
The most complete and most interesting among this school of philosophers was Heraclitus (c.536-470 BC). He was able to think of reality as a flux.
This view is basic also to Bergson. He was famous for saying, "You cannot step twice into the same river; for fresh waters are ever flowing upon you." (52) This led him to further logical implications by which we could imagine two points in a flowing river cancelling out dialectically and yielding what is Good, instead of merely remaining within the dual horns of an implied dilemma. When the situation is fully understood in its abstracted and absolute context, he may be credited as having said something paradoxical, as when Shakespeare said in As You Like It: "Sweet are the uses of adversity".
We now quote Heraclitus:
"It is the opposite that is good for us.
It is not good for men to get all to get all they wish to get.
It is sickness that makes health pleasant; evil, good; hunger, plenty; weariness, rest." (53)
He further referred to the ascending and descending movements between elementals, with Fire as the centralizing factor. Such a view is full of significant suggestions for the detailed implications of the structuralism we are trying to analyze and understand, together with its more dynamic aspects. Once again we refer to this interesting hylozoist who wrote:
"This world which is the same for all, no one of gods or men has made; but it was ever, is now, and ever shall be an ever-living Fire, with measures of it kindling, and measures going out.
The transformations of Fire are, first of all, sea; and half of the sea is earth, half whirlwind ....
All things are an exchange of Fire, and fire for all things, even as wares for gold and gold for wares.
Fire is want and surfeit.
Fire lives the death of air, and air lives the death of fire; water lives the death of earth, earth that of water." (54)
We shall soon be referring to modern developments in thermodynamics which, as we shall see, will bring into evidence fundamentally the same structural outlines in a more direct and convincing fashion. Even the world of machines, properly understood, reveals to us the pure and thin vertical axis which, like "Ariadne's thread", passes through the whole horizontal situation of machines, giving to the totality of such a logical parameter or reference the same status as the "thin and pure" Infinite of the Eleatics. Before coming to such a pure notion where there is no duality implied at all, we are still, in this section, concerned with the nature of the "two-fold effort" referred to by Bergson. One of these refers to the mind, and the other to matter, as is very clear from his words. They refer to metaphysical and physical factors respectively. It would not be wrong to think of other philosophical contexts referring to the same as the intelligibles and the visibles, or in the context of modern science, as the calculables and the observables. Whatever pair of terms might be used they must refer to the horizontal (practical) and the vertical (pure) aspects of the same total knowledge-situation.
When epistemology has been properly rid of its subjective as well as its objective prejudices and reduced to homogeneity in terms of self-consciousness (which should also cover Cosmic Consciousness) we have a schematic picture in which matter and mind meet in mutual transparency and, by participation, articulation or mutual insertion, attain the neutral normative Absolute. The change-over mechanism between physics and metaphysics is both psycho-physical, trans-subjective or inter-physical at one and the same time. This is where "double becoming and double passing away" of things mentioned by Empedocles begins to have some meaning. Further analysis of such a four-fold mechanism cannot be carried on easily. Electromagnetic pulsations, the growth and division of organisms, and even the beating of the heart, all conform to this fourfold alternating pattern like a figure of eight with a double phased movement to which all natural processes conform.
21. POSSIBILITIES AND PROBABILITIES MEET IN THE MATRIX OF RELATION-RELATA
It is evident from the words of Bergson, Eddington and Wittgenstein, and of other pre-Socratic philosophers (quoted on pp. 56, 57, 73 above, and following below), that we come face to face with an astounding truth by which all significant natural ideas are capable of being treated as valid truth, compatible with the Absolute. There is thus nothing to be proved as everything could be left to prove itself. Such a neutral ground is what properly belongs to the Absolute which is the seat of a double certitude.
Both the perceptually understood sets of relation-relata complexes, treated together with their corresponding conceptual sets or counterparts, fill the totality of the content of consciousness at any given time. Their movements and adjustments in mutual relationship, within this total domain of significant discourse treated as a unit, take place as between nominalistic and perceptual elements having the status of real mathematical "things". Reciprocity, complementarity, compensation, one-one correspondence and cancellation are all notions proper to such a context, as we shall see. When reality is treated on the lines of an Heraclitian flux, then between any two points of the flux a dialectical cancellation of counterparts or opposites takes place. This will always yield some value-factor existing beyond paradox. By the end of the previous section we expect we have said enough to make all these bold ideas acceptable enough for us in our attempt to reconstruct a Science of the Absolute. The reader will notice that we are here standing on very subtle ground to be understood only, as Sankara said, by those persons endowed with the quality of uha-apoha, or the special type of intuitive or imaginative mind capable of going backwards and forwards in a double process of dialectical thinking. This two-sided corrective mechanism is not unlike the feedback arrangement or retroaction understood in the context of modern cybernetics. Such a double-sided method is also sometimes referred to as properly belonging to the combined method of agreement and difference known to Vedantic logic.
It is very basic in its methodology, being much favoured by Vedantic speculators like the author of the Pancadasi. The technical name for such a method is anvaya-vyatireka. Here the reasoning moves very subtly and imaginatively, going first to possibilities which are vertically arranged in a mesh or matrix as it were, and then backwards to the corresponding horizontal counterparts which represent the total field within which probabilities have to establish themselves.
When we say something is probable we imply at once that certain other things belonging to the same context are improbable Thus there is a negative and a positive probability, as well as a negative and positive possibility within the "matrice" system. When this is looked upon as a logical matrix, scientific thought is obliged to look up or down, inductively or deductively, yielding whatever certitude it is possible to obtain within the four walls of this structure. We now know also of the mysterious Gaussian curve of probabilities which is like a letter S with a long sloping line curving at its top towards the right and at its bottom towards the left. This figure has emerged as a structural secret and is being extensively used at present by many modern writers in the prognostics of statistical probabilities. It has become a fecund, beautiful and powerful weapon in the hands of modern speculators who wish to adhere as closely as possible to the norms and standards of science.
We could treat this same curve together with its natural negative counterpart to complete our schematic process of becoming. We could try in this way to fit these two aspects into the fourfold or quaternion scheme or pattern about which we have already given indications. Here is a changeover from the metaphysical to the physical side of the total knowledge-situation, implying an intersection, as it were, of two circuits at the point of origin. Treating together probabilities and possibilities, we find roughly emerging into view a structural pattern move or less resembling a figure-of-eight. The horizontal probability curve has here to be understood as modified by its own considerations of vertical possibilities. The full justification for such a figure-of-eight put forward here stands, we admit, on the ground of the uha-apoha (intuitive insight) which, according to Sankara, one must possess in order to be fit for the study of Atma-Vidya or the Science of the Self. If we should also plead for the same concessions which we have seen Einstein himself plead for, in the matter of reconstructing his own Unified Field Theory (see p.71 above), it would perhaps be conceded to us at this stage that our own speculations in the pages that follow could claim as much validity as any speculation could ever have when its certitude is made to depend on possibilities and probabilities at one and the same time.
All men inherit, consciously or unconsciously, many general ideas having their source in some imaginary Omega point in the total knowledge-situation called human understanding.
Descartes would have called this Omega point God. In the Chandogya Upanishad (VI.3.2.) it is stated that names come from the same source. (55)
Dionysius the Areopagite, the early neo-Platonic "Christian" theologian, also considered this the origin of the "Divine Names" and says:
"Thus then, the Universal and Transcendent Cause must both be nameless and also possess the names of all things in order that it may truly be an Universal Dominion, the Centre of creation on which all things depend, as in their Cause and Origin and Goal." (56)
In a very admirable analysis of the origin of general ideas from deep-seated instinctive levels of life in general, Bergson builds an interesting hypothesis reaching up to all higher levels of a vertical line leading to the most abstract of general ideas used in significant discourse in human life. The instinctive and the intelligent levels conform to the horizontal and the vertical axes respectively. This becomes clear when we read the following:
"This is all we wanted to say in order to justify a classification of general ideas which puts on the one side the geometrical and on the other the vital; the former bring ing with it resemblances, the latter identity." (57)
At a high level of abstraction and generalization, when applied to the domain of inert objects, even entities of physics or chemistry could attain the status of general ideas when, for example all green objects in the universe anywhere and at any time are classed together under a certain systematized reference number as an universal concrete. When further abstracted and generalized even beyond metaphysical levels, one's own theory could even come to resemble the classical theory of the divine origin of names. Bergson, as an instrumentalist and a pragmatist is satisfied in not going so far in indicating such mythological or theological limits of his own theory. How he modifies such a classical tendency, and avoids myth, could be clearly seen in the following:
"All general ideas derive benefit from the objectivity of some among them. Let us add that human industrial effort to make things does not exercise itself only on matter. Once we are in the possession of the three kinds of ideas which we have enumerated, above all the last, our intelligence takes hold of what we might call the general ideas as it pleases. It commences naturally with what could be favourable to social life, or more simply to what is related to social life. Then come those which are purely speculative and thereafter what one constructs is for nothing but pleasure only. But in respect of all these concepts not belonging to one or the other of the two categories, that is to say in respect of a great majority of general ideas, it is the interest of society together with the interest of the individual, it is the exigencies of conversations and of action which preside over their birth." (58)
We see here Bergson following the method of ascending speculation rather than describing the birth of general ideas descending from some high divine source as has been more usual in earlier philosophical tradition. Bergson's method is in keeping with a more scientific way of thought wherein metaphysics is treated as a natural prolongation of physics. He has also this most interesting statement about the general idea:
"Undoubtedly one should be able, without difficulty, to conserve the general idea of a general idea if one chooses. Behind the work of the spirit, which is the act, there is the function." (59)
Human knowledge is a resultant of a descending set of nominalistic ideas coming from above, and an ascending set of corresponding schematic abstractions referring to visible reality. When they meet and fuse, all things may be said to emerge and gain the status of things that are both experienced and conceived at one and the same time. In this process of fusion of subtle elements there is a vertico-horizontal exchange within a four-fold structure which we have analyzed elsewhere. There is also a constant circulation and osmotic interchange as between the contents of the two conceptual and perceptual compartments within total consciousness, separated as it were, by a living film placed between names and their corresponding forms. The schoolboy's effort to link names and forms comes from having to break through this separating film. There are many names and forms to be thus vertically coupled but, on final analysis there could be only the name-form-complex in the fully absolutist context. All multiple names and forms spread horizontally with a somewhat monadologic structure on the surface of the general ocean of names and forms." (60)
The central vertical line which cuts through and across this pluralistic horizontalized realm of names and forms comprises all possibilities in the universe in the process of its grand becoming and is, in its lower half, immersed, as it were, in an ocean of probabilities. This thin and pure reality below the ocean's surface corresponds to the notion of the Nous, as developed in Pre-Socratic philosophy. Above the level of the water, ontological aspects give place to transcendental or teleological aspects and necessary factors become related to the full freedom of contingency in the world of names. We have here the corresponding world of the Logos, whose apex is what we have referred to as the Omega point. In the intermediate zone where the necessary aspects meet the contingent aspects, we have the zero zone of indeterminism or incertitude, and this is where the saying, "The wind bloweth where it listeth", becomes fully valid.
Such is the outline structure that emerges roughly for our present discussion. Further and bolder elaborations of this same structure, which is bound necessarily to depend on axiomatic general thinking rather than on strictly experimental thinking, will follow in these pages. For the present let us say that we have more or less justified the assumption of the alternating process taking place as an osmotic interchange. We have tried to outline the conceptual and perceptual elements. Each one is a relation-relata complex in itself whose value-essences change over from one side to the other conforming to the pattern of a figure-of-eight where interests change over from one side to the other of the total fourfold structural situation. To further justify the vertical axis and the figure-of-eight, let us once again quote from Bergson, who followed similar lines of schematic reconstruction concerning the two rival systems of references S and S' revalued and presented in a more unitive or absolutist form to bring out the shortcomings of Einsteinian relativism. We can see how he changes space itself, not into a space-time amalgam, but into a single vertically absolute parameter:
"We shall be changing nothing in the result and we shall be simplifying our exposition in. supposing that the space of the systems S and S' is reduced into a unique dimension, to a straight line, and that the observer in S' having a vermicular form inhabits a portion of this line." (61)
The absolutist reduction of space-time into one dimension with a place even for an observer could not be better schematized. It was no wonder therefore that after publication Bergson had ultimately to suppress this work in which he gives us a bold and imaginative picture of a vertical axis linking up two rival systems of reciprocal reference.
On page 204 of the same work he also refers to a helicoidal structural form, which we have quoted elsewhere.
In electromagnetic radio diffusion we also have the basic pattern of a pulsation comprising sinus functions belonging to a simple harmonic motion, wherein amplitudes and wavelengths enter together for propagation purposes. When the twin functions are put together there results a horizontal-cum-vertical figure-of-eight. These figures are familiarly seen in books dealing with alternating pulsations of electromagnetic diffusion of energy. Life itself is a pulsation, and outer Nature reveals the same alternating features of combined probabilities and possibilities. The Gaussian curve, when understood with its actual and virtual implications together, suggests this same figure-of-eight structure as near as possible. In respect of the frequency of clear and cloudy days, Edna E. Kramer in her book on mathematics writes:
"There are many clear days and many days in which the sky is completely overcast, but relatively few partly cloudy days..,..
Although we no longer expect to find so many approximations to the normal curve in nature, the Gaussian distribution is still of great importance in the theory of probability." (62)
The total cosmo-psychological situation in which human life is cast is subject to this grand twofold "respiration" to put the same truth in the more poetical and imaginative language of the Upanishads. All this we admit is a bold form of scientific speculation justified only by reasons based both on possibilities and probabilities, as we have already explained.
22. THE DIALECTICAL AND STRUCTURAL RELATIONSHIP BETWEEN MAN AND MACHINE
Cybernetics is a new and interesting development in the world of machines. Some people are more easily enthused than others about the possibilities of what the "thinking machine" can do. There are sceptics and believers in the world of the "thinking machine", as there are sceptics and believers in respect of God. About the "'thinking machine" itself let us read what Irving Adler has to say:
"We refer to automatic computers as "thinking machines" or "electronic brains". These terms are dramatic, but not very accurate. They make it seem as though the computers can do the same kind of thinking that the human brain can do. Actually, this is not so. Roughly speaking, there are two kinds of human thinking. There is creative thinking, based on imagination and insight .... There is also routine thinking, that requires no special talent to carry it out .... It is only this kind of routine thinking that a so-called 'thinking machine' can do .... Behind the routine thinking of the machine is the creative thinking of the men who invented it." (63)
Man and the machine belong together in the overall context as dialectical counterparts.
Modern "teaching Machines" show that the Black Box contains the complex and subtle electronic mechanisms at the basis of the choice between contingent and necessary elements of information that are fed into it. These work backwards and forwards on a structural field of possibilities and probabilities and are able to respond in a very subtle manner to the reaction coming from the person who is being taught. His hesitations and even his inhibitions causing delays in the process of learning are recorded and 'remembered' by virtue of the workings of the Black Box. (64)
In other words, the Black Box treats the learner as a Black Box counterpart of itself. Thus, there is a mutual exchange of information entering and leaving the machine, and circulating in a sort of double vectorial or projective space. Between the mechanical considerations which are automatic to a high degree, and the possibilities of bridging the gap at every moment, there is a control mechanism corresponding to the intermediate factor of intelligence. Thus, there are here some common structural elements belonging both to the man and to the machine in cybernetics. This is what we are more directly interested in than in deciding whether cybernetics is or is not a wonder in itself.
Between the horizontal world of machines and the element of human intellection, which is, as it were, implied, there runs a vertical correlating principle which can. be called a logical parameter. When schematically compared to the abstract concept of entropy we can recognize at least this one very important structural feature as common to cybernetics and thermodynamics, besides others that can be graded in resemblances of lesser importance. From simple computers or adding machines up to more truly electronic gadgets that can guide aircraft and process information, there is now a great range of variety in the world of cybernetics. This science is being subjected to complexity elaborations by engineers who are able to enter into its possibilities with their inventive genius and find themselves at home in this ever-widening field so full of promise. This is not what directly interests us here. What should interest us, as it should interest the philosopher rather than the engineer; is the logical parameter common to cybernetics and thermodynamics which opens up vast possibilities for the structural integration of different scientific disciplines.
It was Descartes who compared man to a machine. Everybody knows that some joints, such as those that articulate the arm of a man, resemble a machine unit. At first sight such a dualistic attitude of separating man's body as a machine from his own mind could be thought of as a failing on the part of philosophy. There are even persons now who seriously think that Descartes was himself open to this charge of dualism and thus not a true philosopher who stood for one truth for both body and mind.
The participation of body and mind is the one basic problem that every philosopher is called upon to explain. The author of the famous Cartesian correlates tried to reveal in his own way the nature of this vertico-horizontal participation. In this matter he used the machine merely as an analogy, and the charge of dualism cannot justly be attributed to him. What he did was merely to think mathematically and schematically of the two aspects involved, by which structurally, man and machine could belong together to the same logical context. The soundness of the Cartesian analogy can be seen from what he wrote:
"You may have seen in the grottoes and fountains which are in our royal gardens, that the force with which the water moves when issuing from its source is of itself enough to set various machines in motion and to make various instruments play or utter words according to the different arrangement of the tubes which convey the water. We may compare the nerves of the machine which I am describing with the tubes of the machines of these fountains, the muscles and tendons with the other engines and springs which move the machines, and the animal spirits, the source of which is the heart and of which the cavities of the brain are the reservoirs, with the water which sets them in motion. Moreover, breathing and similar acts, which are natural and usual to the machine and depend on the flow of the spirits, are like the movements of a water-clock or mill, which the ordinary flow of water keeps continually in motion. External objects, which by their presence act on the sense-organs of the machine and so determine it to move in different ways according to the disposition of the brain, are like strangers who enter one of the grottos and are themselves the unwitting causes of the movements they witness." (65)
Bergson, himself as an instrumentalist, naturally treats man and machine as belonging together as counterparts. This is revealed in the last sentence of one of his most interesting works dealing with morality and religion, which reads:
"Theirs the responsibility then, for deciding if they want merely to live, or intend to make just the extra effort required for fulfilling, even on their refractory planet, the essential function of the universe, which is a machine for the making of gods" (66)
To associate man with the machine is not a new departure in philosophical thinking. Pascal even points out how a mechanical automation representing a monkey can have equal status with any living monkey in all matters except those of volition and memory. To bring this point home we read the following:
"An aspect of the brain's greater complexity is the great size of its memory capacity. A large modern computer has a memory capacity of one million bits. The memory capacity of the brain has been estimated at 280 billion billion bits. So the brain's memory capacity is 280 million million times as great as that of any existing machine." (67)
What we have said so far is in order to bring man and machine together into the same context as counterparts, in a schematic or mathematically understood sense, without any implied dualism between mind and matter.
Now let us turn our attention for a while to what experts in cybernetics themselves claim about its excellences. We have to keep in mind when doing this that there is, between the two counterparts, a thin and pure vertical line, called a logical parameter, or otherwise more mythologically referred to as "Ariadne's Thread," by which she successfully guided her lover Theseus through a complex labyrinth full of danger at every step. This is the thin and pure vertical axis which it is our object to reveal and clarify here in all its implications.
The thermodynamic notion of entropy refers more directly to disorder than to order in the universe. Order has always to be created by living intelligence whether on the part of animal or man. The so-called intelligence of the machine is the same essentially as that of animals in the matter of creating order out of disorder, and it is therefore that some thinkers have employed the notion of negentropy which is opposite in effect to that of entropy in physics. Entropy and negentropy treated together refer to one and the same thin and pure vertical axis or logical parameter. We can imagine a thin thread as passing from the zero point towards which all entropy of the universe reaches, as stated in the second law of thermodynamics. This tends to ascend by its power to conquer disorder through a vertical line, passing from mechanistic to biological aspects and finally to reach beyond to the world of general ideas in which the human mind alone finds the interest to live in the world of higher speculation natural to man.
The various stages of ascent have already been reviewed by us in the words of Bergson (see page 93 above). A lower zero point could also be thought of according to the structural language we have developed for our purposes in the present work, and has more in common with the Nous than with the Logos as we have pointed out (see page 84 above). As we proceed, we shall further elaborate on this Alpha point which, when produced vertically, will pass through the neutral zero point before finally reaching what has now become the fashion to call the Omega point. Writers like de Chardin believe in it and consider it the point where God resides, as is evident from his writings. (68) The thin line joining the Alpha point with the Omega point covers the range of all possibilities in life in the context of the Science of the Absolute. Describing the subtle basic principle underlying the world of information of cybernetics, Norbert Weiner, who may be said to be "the father of modern cybernetics," explains as follows:
"If new information changes a set of contingencies having an original total probability P into a set with a total probability p, the amount of information is something of the same nature and dimension as entropy in statistical mechanics, but it is measured with the opposite sign. Thus, information theory becomes a branch of statistical mechanics and the second law of thermodynamics takes the following form from the point of view of the information theory. Any processing (of) information from already existing sources may decrease, but not increase, the numerical measure of this information" (69)
In the above quotation, besides putting the notion of entropy, to which we have just referred, into the context of the world of information, Weiner puts his finger on the most fundamental philosophical secret by which cybernetics as a whole works. We see him refer to statistical probabilities of two grades: one he distinguishes with a capital P and the other with a small p. The distinction he wants to establish cannot be quite clear to us, except when we follow our own line of thought, by which the more general ground of all probabilities can be referred to as a possibility because one unique possibility suffices to establish its truth; whereas for probability many successes are required to establish the truth by statistical average. The former is nearer to the ground of absolute truth than the latter where plurality prevails. Possibility therefore belongs to the vertical in the structural language adopted by us, and probability is ranged horizontally in its less rich or more indigent pluralistic ground. The so-called "thinking machine" has implied within it also the principle of homeostasis which resembles normally the principle of thermodynamic equilibrium. Action and retroaction through a governing control mechanism help the machine to choose carefully between the vertical possibility and the horizontal probability in its backward and forward probing efforts, similar to the groping of a blind man.
Probability must always presuppose possibility. We now quote from another authority on cybernetics:
"'Intellectics', as used by us in the present work, means the theoretical science of effects. The notion of machine thus truly represents the sector of practical applications, while at the same time the two fundamental criteria, which are to be attached in an a priori manner to the notion of machine, are beginning to reveal themselves in the following way:
1. Its logical structure, that is to say its functional scheme, in which a machine could be a simple link in a chain of transference alone or a passive or active and more or less complex channel.
2. Its physical structure outlining the manner in which the functional scheme in question is being materialized and which in the present case as the physical characteristics involved in such a realization.
When one considers the unbelievable variety of possible structures, the diversity of means at the disposal and that of admissible precision in the production of effects, it truly appears that the number of machines exceeds that of all the chemical combinations from simple elements we could imagine.
This however is not important, the "logical" parameter being the thread of Ariadne which enables us to move without error in this universe of machines." (70)
As we see, the importance of this quotation lies in the fact that the writer is able to separate the logical aspects from the mechanistic ones in the total knowledge-situation.
Thus according to well known authorities we are justified in thinking that there are important structural elements, one of which is vertical and the other horizontal. What is more, both are common to man and machine. Possibilities and probabilities enter into a subtle interplay resembling the same problem-solving function that both machine and man may be said to accomplish. The alternating process of thinking, which resembles a probing effort, may be thought of as resembling the same double circuit implied in all life-pulsations or functions such as that of the beating of the heart.
Thus cybernetic structuralism as a publicly understood discipline, steps into the breach where thin speculation previously prevailed with its own definite and tangible contribution supporting the claims of schematism, structuralism and the double movement at the basis even of thought in the context of a Science of the Absolute.
23. SEMANTIC POLYVALENCE OF THE WORD AND ITS MEANING
The transition from the world of cybernetic information to that of semantics is an easy one. In the pure domain of semantics the word and its meaning cling together inseparably as two coordinated or complementary and reciprocal elements. Treated as information these two factors have the same status, as Kalidasa has implied in the very first verse of his epic poem "Raghuvamsa":
"United as word and meaning
In the interests of proper word-meaning,
I salute the twin-parents of the world,
(Both) Parvati and Paramesvara."
These two word-aspects clinging together as the twin parents of the world as Parvati and Paramesvara (i.e. Siva) are from the Indian context. The Bible, in St. John's Gospel, says that the word was God, and that all was God. It also speaks of the distinction between the living word and the dead letter. Semantics is a modern science with very ancient origins, known to be very important in bringing out the full absolutist status of God or Reality. We have spoken of information and noise as two distinct elements entering into cybernetic control and communication. The same two elements, one vertical and the other horizontal, are distinguishable in semantics. Both are to be treated together on a schematic and nominalistic homogeneous matrix.
Thought processes that are so essential in communications should be understood in all their structural and linguistic implications. Linguistics is a subject in which theoreticians can easily be misled and lose themselves in painful and vain labours, This is brought into evidence by the attitude of the Linguistic Society of Paris which openly discourages any study of the origin of language. They have evidently had enough of this subject to make them turn away from its study because of the fantastic theories generally put forward. But when approached with the structure of language, understood in broad outlines at least, semantics can become a very fruitful and even precise discipline, as it has tended to become in recent years. Many are not able to respect the structural implications of semantics and wander far and wide into sterile bypaths.
The origin of language is one of the most difficult theoretical problems that we face. Some, like Ullmann, think in terms of the basic phoneme (a semantic unit of sound) in any one vernacular or language, as when he refers to the 44 or 45 phonemes in the English language. (71) Others analyze gestures and primitive sounds. A great deal of present literature of this kind has really no real value in our eyes, nor are we interested in finding a new universal language artificially constructed. Any universal language must be based on structural scientific principles which properly regulate the science of semantics when normalized and understood in its own absolutist context.
In the Sanskrit tradition, we have the Panini Darsana which refers to the central absolutist notion of sphota (the essence of meaning bursting forth) as understood by the great grammarian Panini.(72)
Word and meaning reside together in the most generalized and abstracted form here and meaning itself is, as the word sphota implies, a bursting forth of a notion with sufficient clarity, within consciousness. The syntactical aspects of language involving units of orthography and etymology have been variously considered as contributing synthetically or analytically to this bursting into meaning of words and phrases. The Purva Mimamsa Sutras enter into this subject in great detail in the context of Vedic exegetics, under the titles of Bhasha-Pariccheda (The Analysis of Language) and Vakya Vritti (The Functioning of the Word). These enquiries are carried over into Vedantic exegetics, and even pressed into service for purposes of philosophical criticism by Sankara himself in his famous bhashyas (commentaries) on the Bhagavad Gita and the Brahma Sutras. This is quite justifiable because the Absolute itself may be said to belong to the order of abstraction and generalization to which the word also belongs. (73) The Absolute cannot give up all its proper implications, ranging within the limits of an actually objective entity to a most comprehensively abstracted nominalistic notion, without itself being reduced for methodological or epistemological purposes to the same order, or common status, as that of the word, where alone matter and mind factors can meet on homogeneous neutral ground.
The word is sometimes called a verb because it represents the most living aspect within the syntactical setup of language. Each verb must have a noun or pronoun as a subject or an object and be related to, or be modified by, adjectival or adverbial adjuncts or complements with conjunctions and prepositions thrown into the bargain, in order to make significant meanings emerge from words and phrases. Such meanings can have a fact-value, a truth-value, or merely a logical value without reference to any outside facts. Syntactics vary from language to language and between the smaller frontiers of vernaculars, giving to the world of linguistic discourse a patch-work appearance through frontiers and sub-frontiers, overcovering the globe. Here it is that we have to think of the difficulty of a traveler passing through these patches and finding that every time he crosses a frontier he has to bear the agony of learning to match words with their corresponding objects. These agonies resembles the tribulations of the schoolroom to which we have referred to in one of our earlier sections (see page 15 above).
Learning is thus a process involving much trouble and where the school master's rod is also to be imagined. It takes place altogether within the mind of man and can be thought of only as moving up and down in a pure vertical axis.
The agonies of learning are not evident to the eye except perhaps in the form of school-children's' tears. It is an inner process, and modern linguistics tries to distinguish it by what it calls semiosis. When we travel more internally in word-value significance into the domain of general ideas where abstract concepts like that of God become important, the tribulation of the person who has to correctly match word and meaning is greater than that of the elementary grades of the schoolroom, where it would suffice to bring together words and their corresponding visible objects. The process of learning, where general ideas are grasped, is a wide and laborious one, covering the whole range of what is called a liberal education. A man of fully liberal education in the correct sense of the word, often tends to be a rare human being. The vertical axis implied in the amplitude of his studies is a long one, reaching from vague ideas, filled with emotional import only, to clearly represented geometrical outlines of a fully public and mathematically valid status. All the intermediate grades belonging to the range of this vertical amplitude have been analyzed masterfully by Bergson in the passages already quoted (see pp. 92-93 above)
These passages of Bergson indicate for our purposes the broad outlines which must suffice in these preliminary considerations. Thus so far from our discussion we can easily recognize two distinct aspects of semantics. One belongs to what is now recognized as the syntax of language, which deals with conventional relations of words, where relative pronouns, prepositions and conjunctions are more important than the meaning of verbs. The second refers to deep-seated meanings and admits even of meaning of meanings in the vertical axis where semiotic processes can move up or down. Modern semantics also deals with another horizontal movement, much favoured by behaviourists and pragmatists who tend to look down with disfavour on anything that does not come within the scope of pragmatic or social utility. (74) Their starting model at the basis of meaningfulness is something they call the "handling action," as for example in a workshop where one mechanic asks his assistant to hand him a spanner or some other tool. This is where communication becomes necessary. Such a communication moves again in the visible horizontal level of practical life. We can imagine yet deeper levels than the pragmatic.
In the world of word-meanings, more vaguely and implicitly understood, a horse is able to distinguish a stable from a barn or a bag of oats from one of malt. Although the animal is dumb in respect of the spoken word, the essence of word-content may be said to be implicit even at this subliminal level.
All we wish to make out in this discussion on semantics, which we have already covered elsewhere in our writing, (75) is to bring out the total structural semantic picture in which, as in the world of information, there are firstly pure vertical factors to be distinguished from their own horizontal counterparts. The more verticalized the meaning is, the more it becomes spiritually significant, and conversely, when horizontalized values are accentuated, language lives and moves merely in the everyday pragmatic and utilitarian world of values. We are also interested in bringing to light the schematic implications which unite semantics and cybernetics as it affords us an occasion to show how two distinct disciplines can have a unifying factor between them when their epistemology, methodology and axiology are treated together with equal status in view of a unified Science.
If this is possible, it should also be possible by extrapolation to see the same structural unity between branches of study considered widely divergent at present. We can imagine two Cartesian correlates in the overall structure here, as commonly implied between any two disciplines under reference. Pure information and pure meaning, with further possibilities of the meaning of meanings, would strictly fit into the vertical axis most significant in human. life. The same vertical axis understood pluralistically, as in Monadology, can be imagined as capable of being fitted into this overall scheme with smaller unit axes, in the world of atomic entities where each particular thing is more simply related to its corresponding collective bee-hive world, matching name and form as in the schoolroom. Innumerable units of such a vertico-horizontal structure could be imagined as covering the surface of the globe, making those patches with linguistic frontiers which we have tried to describe above. Concepts will meet their corresponding percepts only when this verticalized element is present as a thin and pure correlate in the mind of the adult or child. Thus we come to have a total, though rough, structural representation of the same structural situation in semantics.
Let us sum up and say that the syntactics and pragmatics, as well as the semiosis where deeper-seated instinctive levels of meaning reside, all have to be linked together by one and the same principle of the vertical parameter along which all semantic processes have to be imagined as taking place. It is all-important for our present study to reveal the nature of this vertical correlation which, if not understood as belonging to the context of the Absolute, will tend to have no serious human significance. The Panini Darsana thus rightly insists on the principle of sphota, where the essence of meaning bursts into being as having a fully Absolute status.
24. STEPS FROM LOGIC TO DIALECTIC
We have seen how semantics and cybernetics together reveal some of the structural secrets of logic. Simple inferential logic, of which even a cow is capable when it welcomes a man carrying a bundle of grass or avoids one with a raised stick, belongs to the instinctive level where living beings adapt themselves to what is favourable in their environment and abstain from what is unfavourable.
Rising from simple inference at this primitive level of logic, we are able to recognize many ascending steps giving each its own variety of logic until we reach the highest kind belonging properly to wisdom. This highest kind of logic Plato calls dialectic, "the coping stone of wisdom." The kind of logic immediately given to us in its first upward step tends to become logistic when some set, class or kind, involving enumeration or calculation affording a choice between alternatives of "yes" or "no" is in question.
When this tendency to divide into choice sets is further accentuated, logistic becomes either calculus or propositional calculus, where many ifs and buts, either-ors, neither-nors, and both or none become the possible varieties of choice, whether as fact-truths or logic-truths. The complications to which logical calculus can enter have been sufficiently revealed to us by the structural features of the cybernetic Black Box to which we have already made reference. The same structural features that we have pointed out can also exist in some sort of mathematical space in the human brain with a one-one correspondence between the Black Box and the brain. Whatever the complications, we can always distinguish between overall possibilities and limited probabilities, filtering or refiltering truths of fact from truths of more logical status, both of which are to be treated indifferently in the world of semantic meaning or cybernetic information.
The analogy of entropy alternating with negentropy as a subtle osmotic interchange of life-value factors, involving a neutral point of equilibrium, can here be composed and fitted into the total logistic situation. When moving in one direction upwards, as it were, in the vertical axis, the limiting case can be said to be that of tautology and at a lower level we can similarly locate the point where contradiction resides, as when we say: "a = a, a = not b", respectively. Binary or multiple alternatives of choice could further complicate this situation through the maze of which we have to see how logistics becomes transformed into its own syllogistic version.
This is where reasoning moves from the general to the particular or vice versa, through the intermediary of a middle term, yielding the famous four-fold limits. Syllogistic reasoning deals diagonally with contradictory and contrary factors in thinking, as some experts have tried to analyze and present to us in a simplified schematic form. Whether contraries presuppose contradictories or the other way about, is however a subtle epistemological puzzle which seems to remain unresolved to the present day. Whatever this may be, it is at this point where contraries and contradictories intersect at the core of the syllogistic situation that we have to locate the implied factor of certitude.
There are thus two kinds of logic in reasoning. The first traditionally formulates its laws under identity, contradiction and the excluded middle. The other variety, of which F.H.Bradley is the most well-known representative in the English speaking world, derives its epistemological background from Hegel, whose approach can be said to be dialectical rather than syllogistic. Although the identity of dialectical counterparts is taken for granted, the law of contradiction is fully repugnant to this way of thinking. As for the principle of the excluded middle, this way of reasoning rather tends to give it an inclusive central position at the core of the total absolutist situation. Bradley had to bravely fight his own battles to establish the claims of his logic within rival traditional schools of his time. His monumental work, "The Principles of Logic", shows how he was able to maintain his own ground against great odds.
We quote the following by Bradley as a sample of this new tradition introduced into the world of logic of his time. Here we attain to the very core of the controversy:
"In England, at least if we go with the fashion, we all have to believe in an inductive Logic, which starting from particular given facts goes on to prove universal truths ....
I am afraid I may lose the reader's sympathy when I advise him to doubt the union of these qualities .... The induction of logicians so far as it professes to make that attempt I shall I try to show will not stand criticism." (76)
These words of an English philosopher and logician who occupied a chair in one of the leading universities of England strangely mention how he feared he might "lose the reader's sympathy." This reveals the tragic element of parochialism in thinking which has always stood in the way of the love of truth for its own sake, which is just what can avoid disasters and secure freedom for man. Textbooks like those of Bain were propped up by strictly untenable arguments supporting induction put forward by thinkers like John Stuart Mill.
The feebleness and inner contradiction or paradox hiding under the noble edifice supposed to have been erected by Mill becomes clearly evident when we examine the validity of the inductive method of reasoning, which has long been recognized as the method proper to General Logic as also to scientific research.
In induction, one travels upwards, as it were, from the particular to the general. The particular is necessarily factual in content, but the inductive generalizations have to be of a different order which can be called abstract or formal, How these two heterogeneous elements can cooperate to yield a central conviction has been a mystery to many except those partial to this school of logic. F.H. Bradley has taken much trouble in the first few chapters of his great work, The Principles of Logic, to reveal the untenability of this approach. Perusal of these successive arguments in the various steps reveals that he has largely succeeded. He makes his position clear in the following way:
"We may briefly recapitulate the result we have reached. An inference is always an ideal construction resulting in the perception of a new connection. So far as this perception of the conclusion is concerned, there is no possibility of laying down rules, and the syllogistic logic teaches a superstition. That logic again has failed to include all the principles of synthesis which operate in construction, and is falsely confined to a single category. It is wrong again as to the number of the premises; and, in insisting on the necessity of a major premise, it is clinging blindly to exploded metaphysics in direct defiance of the most palpable facts. And it makes a further mistake as to the necessity of elision." (77)
In a previous section of this work we have referred to dialectical methodology. We were able to see how the tendency among modern scientific thinkers was to accept the dialectical approach rather than the line of trial-and-error or even inductive hypotheses. Here we have seen how the inductive method is defective even in the context of logic. Recent writers on the subject, such as B.N. Roy, are able to bring to light some of the glaring shortcomings of the logic of both Bain and J.S.Mill.
Roy writes as follows about Mill:
"It is clear that Mill's argument on this point is a petitio principii. He simply begs the question. He assumes the very thing he wants to prove. He says that the principle of Uniformity is "an assumption implied in every case of Induction" - that it is "the ultimate major premise of all inductive generalizations", and yet it is the result of Induction. How can it be an "assumption" and at the same time, a "conclusion" of Induction? Induction per Simple Enumeration also relies on the principle of Uniformity; unless there is an assumption of Uniformity, we cannot in any case pass from the particular to the general.
Another obvious difficulty in the theory of Mill is that according to him, the conclusions of Induction per Simple Enumeration are merely probable while those of Scientific Induction are certain. If the principle of the Uniformity of Nature be the result of an Induction by Simple Enumeration, it can only be probable; but it forms the basis of all inductions, including Scientific Induction, which according to him, gives certainty, But how can Probability be the basis of Certainty?
"These contradictions in the theory of Mill are the result of his empiricist philosophy. According to Empiricism, all knowledge comes from experience and hence, the knowledge of the Uniformity of Nature cannot be an exception - it must also be derived from experience. The fact is that Empiricism fails to give a proper account of the origin of what are called fundamental principles, such as the principle of Uniformity. These fundamental principles cannot be proved but they form the foundations of proof. They are assumed to be true and are called "postulates." The Uniformity of Nature is such an assumption of Induction. Without this assumption, Induction is not possible. it is the ground of Induction and not the result of Induction." (78)
All these considerations go to prove that scientific methodology requires to be revised in the light of some normative notion of the Absolute. When the totality of the steps involved in reasoning stand clearly revealed to us with all its gradations from animal inference to high dialectical reasoning, we shall be able to see that these mark the vertical axis that we have here tried to distinguish. Dialectic in its last stages can be treated both as an ascending and a descending process. If we accept the upper limit of axiomatic a priori sm first, reasoning can descend through postulates or propositions to more tangible realities.
It is not impossible, in principle at least, to adopt an ascending process in the same way as Bergson has done in arriving at the most general of ideas, starting from those directly experienced through intuition by everyone. Reasoning is a double process which finally abolished its own duality by meeting at the core the normative notion of that Absolute, which must necessarily be presupposed by all reasoning.
25. MATHEMATICS REVEALS THE POSSIBILITIES OF A SCIENCE OF THE ABSOLUTE
I. THE MATHEMATICAL FRAME OF REFERENCE
The mind seeks certitude through solving problems, whether one is interested in technology or in such subjects as astrology, involving celestial influences on human life. Mathematics as a discipline belonging to the world of intelligent discourse comes in as an instrument for problem-solving of every kind. Calculables and observables resulting from abstractions and generalizations can attain to a high degree of perfection in certitude in the world of mathematics. Standing on its own neutral ground where one set of observables is related to its own counterpart of calculables, mathematics yields what is called a proof through equations or visible geometric forms, or both. Mathematics has sometimes been referred to as gedankloses denken or "thinking without thought". Hilbert, who has succeeded in giving to mathematics a special geometric discipline of a fully independent status, thinks of mathematics as a kind of game and defines it as follows:
"Mathematics is a game played according to certain simple rules with meaningless marks on paper." (79)
It would be wrong for us to say that mathematics deals with airy nothings. This would amount to saying that although it is full of importance to man it does not refer to that very reality where all problems reside, though it can do so only perhaps with the thinnest of transparent veils. Many grades of veilings of truth are possible. Mathematics is perhaps the last or the thinnest of the obstructions that might be said to hide the full vision of truth from man. The Pythagoreans were not completely off the mark when they thought of the universe as being made up of the same stuff as that of mathematical symbols, such as numbers with their corresponding structures when treated together. Those interested in machines rather than Gods might mistrust such a Pythagorean attitude as something outmoded and mystical. These are the sceptics. Yet there are others who are temperamentally believers and to whom Pythagorean ideas mean something very valuable in bringing man face to face with divinity. Modern developments in mathematics have tended to open large vistas in both these directions. God and mathematics are being linked together in scientific writings.
The variety of titles of books on mathematics seen in bookshop windows anywhere in the modern world are in themselves sufficient evidence of the doubly enigmatic interest the subject holds on today's intelligent and original thinkers and the inventive minds of modern youth. Mathematics is referred to both as fun and as something earnest. One may find intriguing titles such as Mathematics in Fun and Earnest (80), Mathematics, Queen and Servant of Science (81), Mathematics in Everyday Things ((82), The Gentle Art of Mathematics (83), Magic House of Numbers (84), and Mathematician's Delight (85). In every case we notice an element of paradox. The two aspects of life with which mathematics is necessarily concerned are brought together is in fact the meeting of the visibles and the intelligibles. This is the element that makes the subject so naturally attractive.
The division between physics and metaphysics is itself dissolved when we think of mathematics as a complete discipline in itself, comprising both algebra and geometry. These two disciplines have appeared in the history of mathematics sometimes as rivals and at other times, as in the latest post-Hilbertian developments they tend to come together as partners, the one lending certitude to the other. In this modern tendency to bring them together we find the epistemological and methodological basis for a unified Science.
What is of import in a Unified Science of the Absolute comes into fuller view when we enter the domain of mathematics where all the required characteristics reside together side by side. Whether we think of physics and metaphysics as distinct disciplines or treat them as coming under the same unified science, there are certain categories or items that properly belong to each of them and which can be put together into a total integrated whole.
Philosophers like Kant find use for words such as noumenal and phenomenal, and practical and pure. In physics space-like and time-like realities are referred to in Einstein's relativity. The perceptual and the conceptual can refer to the same two rival aspects that call for mutual or reciprocal treatment as related to each other. The observables and the calculables correspond, term by term, to the visibles and intelligibles of Plato. Each philosopher has his favourite pair of terms, like Fichte's distinction between the self and the non-self. The a priori and the a posteriori refer to the axiomatic and the experimental aspects of scientific thinking. Algebraic symbols may be said to be nominalistic in status while the esprit géometrique of Pascal is perfectly at ease and delights in the world of forms, from which the word "information" as used in cybernetics is itself derived. Whatever pair of terms is used, they can all be fitted into one and the same vertical and horizontal schematic version of the schematism we have so far developed, each pair belonging together as conjugates, as they are sometimes referred to.
For the same reason of schematizing, Hilbert has been called a formalist. The ancient Vedantins of India have summed up the total situation involved by the expression nama-rupa (name-form). This last way of looking at the total bipolar or ambivalent situation which faces us everywhere when we think of an integrated or Unified Science comes very near to that of modern mathematics. Formalism and structuralism are at present accomplished verities rather than something still waiting to be recognized by mathematicians of the future.
As we all know, the most elementary form of mathematics begins with a child who counts on its fingers when adding up simple numbers. What the digits themselves represent as numbers is a starting abstraction forced on the child by the schoolmaster's cane rather than something coming from the child's natural understanding. Elementary school teachers can be very easily aware of this when, for example, a child shows confusion when asked to say how much is left when you take away one number from another. The child lives in a simple world of events and objects and is not at home with such abstractions. The writer himself recalls his own younger brother staring at him in great confusion and dismay at this evidently simple question. When forced to answer he helplessly asked where I had put those items thus taken away. Without knowing how to enter a world of abstraction and generalizations the child could not proceed further.
Number itself is a mystery for the most advanced mathematician. It represents a second degree abstraction from actuality. There are thus any number of degrees of abstraction and generalization possible in mathematics. This is exactly what makes for both the tears and delights of the subject. The most elementary stage of mathematics can be imagined as a vegetable or grain market on the ground floor of a tall building such as Woolworth's department store. This is the level where normal arithmetic prevails. We can imagine successive floors, serially piled upwards and accessible through lifts in the building. This structure is like degrees of purer and purer mathematics treated as a whole. Each degree of abstraction or generalization lies on a level or horizontal floor of its own. Technology involves itself in its own abstractions of abstractions and generalizations of generalizations, till a level is reached in the hypothetical top storey where abstractions become interesting for their own sake. On this higher level applied mathematics parts company with pure Mathematics. The former still refers to values most marketable on the ground floor. After the turning point, about the middle of the building, interests begin to point upwards, as it were, to the purer delights of mathematics, where it is a game rather than a toil. Further storeys can be imagined which we can pass through by either local or express jumps to the pinnacles where pure mathematics resides. Here it is fully a game as Hilbert defined it. Mathematics can either prognosticate with expectation or calculate with regrets to gain experiences from the past.
We have thus a prospective and a retrospective vision evoked from any point on a vertical scale of the total range of mathematical thinking, which can be imagined as linking the lowest horizontalized version of the discipline with the highest which deals with non-earthly human values. We can further imagine a possible extrapolation or interpolation of the thinking process involved in either an upward or downward direction. Each person chooses what he is most interested in, whether in old age or in youth, and fits his life into the various levels which must always have their vertico-horizontal component factors. No-one can escape anything and each person is caught in situations where inner urges attract to corresponding outer factors. We can thus imagine a scale of values proper to the type of each individual. This vertical principle has been called by some mathematical experts a fil conducteur, (guiding thread). Speaking of the virtues of modern projective geometry, and its easy operation, G. Verriest states the following:
"In projective geometry, there is no such difficulty This science, supporting itself on axioms which are remarkably symmetrical, first places the properties of very simple configurations, formed by points situated on the same straight line; from straight lines, proceeding through the same point and situated in the same plane, and planes passing by one and the same straight line, it progressively passes over to the study of more complicated configurations, while the conducting thread of the demonstrations remains always the same. Notably there is a certain correspondence between the elements of the figures considered. (86)
Of all the innovations in mathematics that of the projective geometry of Poncelet taken together with the one-to-one correspondence of Cantor, have had the most far-reaching repercussions on modern mathematical thinking. There are also many minor contributions which we shall presently review.
II. THE DELIGHTS AND PUZZLES OF MATHEMATICS
The delights and puzzles of mathematics are many and can be reviewed seriously without emotional distortions or intellectual complications only by a sober scientific mind. The possibility of wonder on one side and earthy utility on the other need not, however, be ruled out of the scope even of a fully scientific view. Mathematics presents to us a series of fundamental wonders, innovations, discoveries and inventions, which remain unrationalized to the present-day. We shall now enumerate some of them at random without attempting to be too orderly and fully sequential, so as to show how a Science of the Absolute could be enriched and clarified by its findings.
1. The four operations of arithmetic: addition, subtraction, multiplication and division have never been increased at least arithmetically in spite of all the elaborations brought into mathematics in general. Why should there by only four? In the domain of algebra it was given to the young genius of Galois to prove for the first time that equations of a higher degree than the fourth were incapable of being solved in a strictly algebraic sense. Writing about Galois, Edna K. Kramer remarks:
"Evariste Galois, the Keats of mathematics, settled once and for all the matter of solving algebraic equations. He proved that it is impossible to solve algebraically the general equation of degree greater than four .... Galois developed the theory of groups and applied it to the question in hand. We shall state Galois' great theorem, which established once and for all a criterion for solvability: An algebraic equation is algebraically solvable if and only if its group is solvable." (87)
The fourfold pattern into which mathematical thinking somehow fits is one of the puzzles which Eddington says he cannot adequately explain:
"To distinguish the relata from one another we assign to them monomarks. The monomark consists of four numbers ultimately to be called 'coordinates.' ... Why four numbers? We use four because it turns out that ultimately the structure can be brought into better order that way; but we do not know why this should be so." (88)
This suggests the same principle of the quaternion which is at the basis of the Cartesian coordinates. The same subsists in the form of the points, lines, and angles in the context of projective geometry, although the orthogonality between the two coordinates is further relaxed here.
2. The very fact that in modern mathematics there can be equations that "answer to" their own graphic representations is a sufficiently mysterious phenomenon, taken as a fundamental basic feature of the algebra of geometry or vice versa. Why should visible shapes or forms have anything to do with something purely conceptual? This necessarily presupposes a neutral substance, where matter and mind seem to be mysteriously participating through some absolutist medium which is neither wholly matter nor wholly mind. This must possibly imply a homogeneous matrix where alone concepts and percepts could meet, cancelling themselves out in the normative principle of the Absolute. We have already referred to the two possible proofs of the Pythagorean theorem, so as to locate this neutral central zone where certitude in mathematics resides. Cartesian correlates give coordinates with a principle of orthogonality implied between them. Even without this strict orthogonality, laws of physics involving direct or indirect variation of various factors, such as the square and the square root of time or of distance, make of these correlates, even in their improvised sense, a potent instrument of research, endowed with fecundity, power and beauty. These powers seem to be attributed also to certain curves, such as the probability curve known to Gauss, to show how these structural features have far-reaching possibilities in forming hypotheses, laws and theories to be later verified or confirmed by observed instances, as in the case of Einstein's theories themselves.
3. Another of the astounding developments in modern mathematics is traced to the name of George Cantor. About the significance of his formulation of the theory of Ensembles, Henri Poincaré says the following (quoted by Verriest):
"The theory of ensembles is, in a certain manner, Mathematics which has rid itself of its substance and is reduced to its pure form." (89)
The implications of this far-reaching discovery are many; such as the notion of transfinite numbers and the one-to-one correspondence, both between transcendental numbers and more immanent ones.
4. Pythagoras brings to light many mysteries in the world of numbers. Space and number seem to be playing hide-and-seek between them, as when Pythagoras points out that we can treat numbers so as to reveal certain shapes when suitably arranged in lines whether triangular, rectangular or pentagonal. For the Pythagoreans this secret discovery has sufficed to elevate the Tetraktys into a symbol of a hypostatic value for adoration in temples dedicated to Pythagorean thought that exist even today. Even the multiplication table of 9 reveals an underlying symmetry, bilateral as well as vertical, where digits can be added or multiplied to reveal structural features, which as it were, enigmatically stare the mathematical theoretician in the face.
At the centre of the table we can clearly see this subtle structural underlying feature crossing over between 45 and 54, each of which when added yields the number 9, while at the same time representing vertically the product rather than the sum, accomplished by a mere exchange of digit positions. The relation between multiplication and addition itself, when closely considered, is a mystery, although ordinary empiricists tend to minimize the wonder involved. Multiplication, in principle at least, inclusively comprises addition, which latter is less rich in number content than the former. In the domain of exponential mathematics, the principle of multiplication attains another height of abstraction. The square of a number results when the number is multiplied by itself. This operation resembles the generalization to a second degree of an already existing general idea. Such a generalizing process can continue into ascending scales of logarithmic succession in the world of numbers. We can also imagine a negative series of the same, recognized in the context of modern complex numbers by the letters j and -j. The latter belong to the side of the base of the vertical axis of which the square root of minus one is a representative and a well known example, Complex numbers themselves contain within their scope negative quantities of a simple arithmetical order, as well as irrationals and imaginary numbers related to a central point of origin. Irrationals, incommensurables and imaginaries can all be fitted together if the idea of the quaternion is kept in mind. We can even think in terms of many dimensions, or in terms of numerous n-legs, some of them time-like and some space-like. These are acceptable to modern mathematicians as a mere amalgam of space-time factors or as more unitively understood, which Bergson would recommend and prefer.
5. The transcendent or transfinite nature of numbers, once recognized, naturally yields its further corollaries which are known as the infinitesimal, differential and integral calculi.
They all deal with an infinite series with an upper or lower limit as in an ordinal series with a number before and after, sometimes recognized as limiting cases. Fractions, whether called vulgar or decimal are said to be the creations of man, while whole numbers have been referred to as coming from the mind of God. As Descartes explained, order and measure constitute the totality of mathematics, reducing everything to two final categories. When order is thought of we refer to the vertical component, and when measure is thought of, it is horizontal, quantitative and arithmetical. There are universal groups or ensembles in an infinite series which, when taken with a zero, refer to proper and improper elements. These between them distinguish respectively the same horizontal and vertical aspects in the world of mathematics. Modern mathematicians use terms which have attained an ultimate degree of abstraction. They speak of variables and constants as the operator or its functional aspect moving invisibly between proper and improper, known or unknown elements. The definition of a point and its indication as a location without dimensions by the letter "p" is perhaps the most elementary of schematic mathematical entities which is thinkable and perceivable at once. In such a notion, fundamental to mathematics, we nearly attain the visible Absolute.
6, Another interesting discovery or innovation, or at least departure from conventions, is the introduction of new structures for space. When classical definitions of space became inadequate for many observed facts, Riemann questioned the Euclidean postulate of parallels and introduced a space whose structure admitted of no parallels. Lobachevsky on the other hand, conceived of a space in which many parallels could exist side by side. Reimann evidently thinks of a spherical curvature for space, while Lobachevsky rather in terms of a vertical axis. Minkowski puts space and time together into a pattern which includes four dimensions instead of three. These innovations are still questionable, although Einstein and others tend to treat these mathematicians with the kind of respect that is given to gurus in India.
Why scientific people should have this preference towards certain persons who break conventions is not very clear.
7. Another set of innovations refers to vectorial space. When measured with arithmetical units, this vectorial space gives directed numbers that are scalar in status. When this scalar quality is further liberalized, we get purer vectorial space of a more qualitative order. When the rigidity of such a treatment is relaxed to a further degree, we get tensorial space with its further implications of spin or calculus. How such liberties taken with space can be justified is a mystery only known to the high priests of mathematics.
We have reviewed some of the wonders, inventions, discoveries, and innovations in modern mathematics; some more arbitrary than others and some which are only further conclusions derived from already accepted postulates. We have italicized some modern terms employed above (see p.134) because of their special interest to us. They tend to prove what O.G. Sutton points out as the role of mathematics in general, which is that of revealing the underlying relational structure of actual experience:
"The first task of mathematics is to provide a convenient and accurate method of summarizing experience .... without some conversion of this kind it would be impossible for the mind to grasp the complicated pattern revealed by the laboratory experiments, and science would be hopelessly lost in an ever-increasing maze of seemingly unrelated facts.
To sum up, mathematicians are no respecters of tradition; but incorrigible heretics who are prepared to change their ground and invent new systems of thought as soon as the old is seriously challenged ....
The true touch of genius appears only when the new algebra or geometry opens up fresh fields of thought, and this is a very rare event." (90)
Mathematics has to proceed by breaking away from convention as well as by conforming to it. The main stream of mathematics is filled with contributions of many bold spirits, many of whom, like Abel and Galois, were fated to die young.
These spirits felt impelled to depart from the usual conventions, and the best proof of their correctness consists in the fact that their innovations have had success in practice. Pure mathematics thus represents facts when understood in its verticalized version Both the possible versions must have the normative Absolute for reference, based on which alone innovations and liberties are possible.
III MATHEMATICS FALLS SHORT OF THE ABSOLUTE.
Mathematics has to prove its own validity by its wide applicability in science. The kind of mathematics used in the quantum theory of Max Planck at present remains different from the kind required for the theory of relativity. These two theories have to be fitted into one Unified Field Theory which must refer in turn to a unified mathematics. Einstein and others insist on remaining physicists first and philosophers, if at all, only afterwards. Even so, Einstein admits the need for bringing these two rival theories under one and the same mathematical formula, when he says:
"But the idea that there were two structures of space independent of each other, the metric-gravitational and the electromagnetic, was intolerable to the theoretical spirit. We are forced to the belief that both sorts of field must correspond to the verified structure of space." (90)
A close scrutiny of these words will easily reveal that the motive behind his desire to formulate a Unified Field Theory, bringing relativity and electromagnetism together into one mathematical structure, is not altogether in the interests of physics alone. The love of unifying different disciplines is the task of a philosophical mind rather than of a mere physicist who can leave perceptible things to speak for themselves. Einstein's ambition of setting up the Unified Field Theory, although it raised great expectations, failed to convince fellow scientists working on the same lines. A.A. Tonnelat had devoted a whole book to this subject called La Theorie du Champ Unifié d'Einstein-Schrodinger ("The Unified Field Theory of Einstein-Schrodinger") (92), in which the merits of the theory are examined with much reserve about its success. In a thesis entitled Quelques Réalizations de la Théorie Unitaire d'Einstein (Some Findings of the Unified Field Theory of Einstein), written by Marcel Lenoir and presented to the University of Paris in 1962, the same reservations referred to above are clearly stated, as follows:
"The great difficulties which this theory comes up against, seriously limit the expectations that it had raised. Meanwhile, in proposing to unite the field theory asymmetrically to the effects of spin, Sciama and Costa de Beauregard have posed some now and interesting problems which will lead us perhaps to a satisfactory interpretation of the Einstein-Schrodinger theory." (93)
This thesis was presented at Paris under the direction of Louis de Broglie and indicates for our purposes how the ambition of Einstein remains still not fully accomplished. The reasons why he failed have been discussed in a work by Henri Bergson called Durée et Simultanéite, where he points out how Einstein, while insisting on being a scientist, is forced to be what he calls a demi-relativist with a unilateral approach, admitting of no radical reciprocity between a space-contraction and time-dilation which must co-exist if the mathematics of the Lorentz transformation are to be fully accepted by Einstein instead of being partially adopted for his limited theory of relativity.
Bergson further charges Einstein with not giving to the time factor its legitimate place in the mathematical or unitive field structure which he tried to build up. Bergson has discussed these matters in great detail, step by step. We shall have occasion to come back to this admirable work in which a master thinker and contemporary of Einstein not only lays bare the shortcomings of his mathematics, but also suggests how such shortcomings could be remedied so as to give to the notion of relativity its fully revised and radical status. Supporters of Einstein have not refrained from manifesting clearly their repugnance to this criticism by Bergson and it was therefore one of the saddest of consequences to find that he decided to suppress his own book on the ground that he was much misunderstood.
We read in his own words:
"We had once before devoted a book to the demonstration of these different points ....But as the book had often been misunderstood we feel that we should reproduce here the essential passages of an article which was the reason for such misunderstanding." (94)
We find therefore that this whole book has been omitted from his "Collected Works" (Oeuvres), and also that there thus seem to be subtle impediments from unexpected quarters hindering mathematics from attaining a fully absolutist status in its own right. Instead, what seems to be wanted is for mathematics to remain merely a hand-maiden. to physics which in its own turn is committed to relativism as a quasi-philosophical doctrine.
This subtle opposition is also seen to be operative in respect of the epoch-making contributions of David Hilbert who has been called a 'formalist' who pushed the interests of formal thought beyond the scope of practical limits. Yet it is exactly here that we find for the first time algebra and geometry together attaining full status as an independent science. The postulates on which Hilbert's grand work on geometry were based are unquestionable and it can be safely asserted that Hilbertian mathematics, especially its geometrical basis, reaches a maturity by its independence and self-consistency as a distinct scientific discipline basically absolutist in outlook. He was even able to think in terms of a mathematical thing or a universal concrete entity wherein all essential geometrical qualities could inhere. In doing this he pushed further, to its natural limits, the findings both of the projective and topological varieties of geometrical thought.
The broad outlines of his geometry can be summarized as follows:
"He succeeded in extracting the fundamental laws of invariants, laying at the same time the basis of the theory of ideas, the polynomial which plays an essential role in the geometry of algebra and in modern algebra.
His Grundlagen der Geometrie, published in 1899, was orientated towards the axiomatic regulation of the various sectors of mathematics, avoiding all dependence on particular concrete images. While doing this he introduced "three systems of things" called point, line and plane. These objects whose nature is not fixed, fulfill certain relational conditions expressed by twenty-one axioms classed under five groups: appurtenance, order, equality of congruence, axiom of parallels and lastly, continuity.
Without turning his face away from Euclid he thus succeeded in giving a more or less final form to the algebra of geometry. The work of Hilbert has led to other modern notions such as structuralism, which may be said to be its most recent offshoot. The possibilities of this new branch are still to be worked out, but we can already see how structuralism is going to play an important part not only in giving precision to the verification of scientific laws in general, but also extending further into the wider domains of composability; integrating and normalizing speculation in general. Whether bearing on scientific laws or dealing with more general ideas, structuralism can now be expected to link apparently divergent disciplines like physics and metaphysics.
We shall not venture any further in this direction, especially as we have already devoted a full monograph to how a structurally integrated model can serve as the basis of a language of Unified Science. For the present, let us close this section with a quotation from the French "Larousse Encyclopédique", which gives us just those aspects of structuralism which appear to have received official recognition:
"All representations of a particular discipline by means of another put into evidence a structural aspect common to both these disciplines. It is in part the case in a formalizing transcription that the Hilbertian project has exercised an accelerating influence on a complete recasting of a general theory of structure. Here we see an evolution towards abstraction which is in the very nature of mathematical activity. It has above all progressed by the junction which has taken place between the theory of ensembles and the study of structure realized by algebra (other than ordinary algebra, such as qualitative and group algebra, etc.). Present day topology offers us a striking example of this new tendency. The merit for this general recasting of mathematics belongs most particularly to the French School called the "Bourbaki" (95)
The same article quoted above concludes with the following words, which also sum up what we wish to say:
"In short one thus sees the double role that mathematics plays in the progress of the human spirit and on the other hand in the progress of all technology." (96)
We can add to this last sentence by way of further explanation that in the light of our foregoing discussion, mathematical thought follows a vertical axis upward into the domain of metaphysics while descending in the opposite direction into the world of machines proper to physics.
26. THE POSSIBILITY OF STRUCTURAL ANALYSIS INSIDE THE WORLD OF DISCOURSE
Each conscious person is situated inside his proper world of discourse. One of the peculiarities of the Science of the Absolute, in its speculative or observational approach, consists of taking an inside view sympathetically at the core of the situation, which is at one and the same time the subject and the object of absolutist speculation or contemplation. This philosophical attitude has been underlined by Bergson in his "An Introduction to Metaphysics." (97)
Intuition works best and gives the most convincing results only when one is able to take a view from inside the total situation instead of taking many photographs, as it were, of the object seen from the outside. These photographic stills, as Bergson points out, even when put together in great numbers, cannot reconstruct the total reality which living intuition alone can give from the inside. He refers to a man visiting Notre Dame and points out how the best idea of the cathedral is given only to a man who enters into it and thus knows it intrinsically and integrally inside out.
In the Vedanta tradition of India this is referred to as antar-mukhatva or an inward-facing attitude. No outside reality exists without the inner universal observer wherein the observer and the observed have to belong together to the same knowledge-situation. This need to put observed and observer together is now beginning to be recognized even in the Relativity theory of Einstein.
We have in the foregoing sections reached the idea of a common structure underlying all disciplines viewed as belonging to a unified or unitary structural whole. Physics is based on objectivity, while metaphysics has its starting point in something experienced within. If the former is experimental the latter is based on inner experience. In an integrated discipline such as the Science of the Absolute, it is all-important that the universal observer should be imagined as taking his place at the core of a system of reference, having a physical as well as a metaphysical status at one and the same time. That is why Brahma-Vidya (The Science of the Absolute) is often identified with Atma-Vidya (The Science of the Self) in the context of Indian spirituality.
The cosmological "world about us" round this Absolute Self has a status somewhat similar to what modern phenomenology gives it. Phenomenologists refer to it as the world that lies around us with an eidetically representative content. Cosmology, psychology and theology centrally viewed from more peripheral or more central sheaths are sometimes called kosas by the later Vedantins of India.
Thus structurally conceived, we can think of a Science of the Absolute which according to Eddington has a conceptual and therefore a mathematical status only. Even physical science is at present recognized to belong to the world of verbal descriptions, whether through algebraic symbols or visible geometrical structural frames. It is now the concept that matters in the latest developments of the quantum and the relativity theories. Thus it is natural for us to think of the pure world of discourse having merely a schematic status. The foregoing sections have been directed to the justification of such a schematic view of absolute reality.
The possibility of placing oneself by intuitive sympathy within a world of discourse is therefore nothing unnatural to modern scientific methodology. The limits of such a fusion of the observed and the observer are still to be reached in the scientific thought of the West, but we have seen how intrepid spirits like Schrodinger have begun to talk of neutral consciousness where matter and mind meet schematically on common ground. The passage that we have already quoted from him (see pp. 67-68 above) is a sample showing how man and his environment can be treated together sub specie aeternitatis in the context of the Absolute.
Now when we think of the total world of discourse we have to remember two broad structural features. The most evident of them is the one we have referred to as the imaginary line or film separating percepts from their corresponding concepts, whether they refer to abstract or concrete items. There are two distinct worlds of the content of the Absolute in one and the same dictionary, just as a telephone directory can correspond to the number of subscribers with telephones in a one-to-one correspondence. Each concept has its own percept in the total world of discourse. Matching them correctly is the work of schooling or higher education. The task becomes most difficult when general ideas like that of God as a Creator have to be matched with his corresponding creation or perceptual counterpart. These two poles of God and his creation may be said to mark the whole range of a vertical axis where semiotic processes move as it were, in a worm-like fashion upward or downward. Such is the first broad sub-division we have to make. The mortality of man is more than a probability, and even one man killed by lightning fully proves such a possibility. Both have to belong together to a common world of discourse.
Herbartian apperceptive masses can be imagined to be formed at the core of this discourse where two aspects, the vertical and the horizontal intersect. This is where the self or the ego with its total or limited, unilateral or bilateral, lop-sided or reciprocal events in consciousness takes its place. Whatever endures in the form of memory or imagination that is retrospective or prospective takes place in the noumenal axis in the centre. Spread out as a plane with multiple possibilities, like events on the surface of the ocean, we have to imagine an expansive universe of discourse inclusive of all men anywhere, trying to match word with its proper meaning in any one of the thousands of vernaculars that prevail on the surface of the globe at any one time.
27. BERGSON'S OWN STRUCTURAL PROGNOSTICS
We find in the work of Bergson already referred to that he discusses in detail, stage by stage, the shortcomings of the frames of reference employed by Einstein in his two theories of relativity. After a full and careful scrutiny of his arguments, Bergson proposes something resembling a structural model which seems to us to come very near to our requirements at the present stage of our own discussion of structuralism in general. In fact there are two contexts in which we find Bergson boldly anticipating the broad outlines of a structural model. One of them is meant to be more realistic than the other, and without taking into account the reciprocity of time and space more fully, is limited merely to correcting what belongs to the inertial field of Einstein. The other deals with the situation more idealistically and gives to time and space a neutralized unitive and absolutist status. When both these proposals are put together we find that there is a complementarity between them which can be helpful in arriving at a more complete model, which can be called both realistic and idealistic together, serving the requirements of physics and metaphysics at one and the same time.
The realistic picture presented to us by Bergson is to be found in the context of finalizing his arguments in favour of reciprocity as against one-sided relativity. He does this by giving his own revised version of the model which would result when such a reciprocity is fully understood in the light of philosophy in general, involving a schéma moteur. What we should specially note here is that even the colourful material world spread out before our vision is capable of being fitted on to an inner geometrical frame of reference just as a tailor cuts a piece of cloth when fitting a coat. These ideas are familiar to us already from his other works, to which we have made sufficient reference elsewhere in our own writings. Bergson now boldly sums up his position in the following important words:
"We do not wish to prolong beyond measure this introduction. We have however to recapitulate what we have said once before about the idea of a body and about absolute movement: this double series of considerations permitted us to come to the conclusion about the radical relativity of movement, inasmuch as it is a displacement in space. What is immediately given to our perception, as we have explained, is an extended continuity on which the qualities are spread out: It is more specially a continuity of visual extension and therefore of colour. Here there is nothing that is artificial, conventional or what is merely human. The colours would appear to us without doubt differently if our eye and our consciousness were formed differently. There would have been nonetheless, something that should be unshakably real which physics would contrive to resolve in elementary vibrations.
In brief, as long as we speak of a qualified continuity and modified quantity, such as the coloured extension changing its colours, we immediately express without any human convention interposed what we see: we have no reason to suppose that we should not here be in the presence of reality itself. An appearance should be credited as being real as long as it has not been demonstrated to be illusory and this demonstration has never been made in the present case. It was believed that it had been done, but that was an illusion; we think we have proved this. Matter is thus presented to us as a reality, but is it so in respect of such a body, erected as an entity more or less independently? The visual perception of a body results from the fragmentation which we could make on a coloured surface which has been cut out by us in the continuity of extension. It is quite likely that this fragmentation is diversely effected by different species of animals, many of which are incapable of proceeding into it; and those which are capable regulate themselves in this operation on the basis of their activity, and on the nature of their needs. 'The bodies,' as we said already, 'are tailored in the stuff of nature by a perception of which the scissors follow a dotted line on which action would pass.' Such is what psychological analysis tells us and physics confirms it. It resolves the body into a quasi-infinite number of elementary corpuscles; and at the same time it shows such a body to be related to other bodies by a thousand reciprocal actions and reactions. It thus introduces into it as much of discontinuity, and also it established between itself and other things as much continuity that one guesses as amounting to what is artificial and conventional in our separation of matter into bodies. But if each body, taken in isolation and stopped where our habits of perception bring it to a termination, is to a great extent a conventional being, how could it not be the same with movement considered as affecting this body in isolation?
As we have said there is but one motion which can be seen from inside and of which we know that it constitutes by itself an event: this is the movement that translates and presents itself to our own proper effort. Elsewhere when we see a movement being produced, all that we are sure of is that somewhere a modification is accomplished in the universe. The nature and the exact place where this modification takes place eludes us; we could only note certain changes of position which are its visual and superficial aspects and these changes are necessarily reciprocal. All movement - even our own inasmuch as it is seen from outside and visualized - is therefore relative. What is more, it goes without saying that it is only about ponderable matter with which we are here concerned. The analysis that we have been making sufficiently makes this clear. If colour is a reality, it should be the same with oscillations which take place in some way at its interior: should we, because of its absolute character still call them movements? On the other hand, how should we place in the same rank the act by which these real oscillations, which are elements of a quality participating in what has an absolutist status as quality propagating itself across space, and the displacement which is altogether relative and which is necessarily reciprocal, as pertaining to two systems S and S' cut out more or less artificially in matter? One speaks of movement here as well as there; but has the word the same meaning in both cases? Let us rather say propagation in the first case and transport in the second: it will result from our earlier analysis that propagation should be profoundly distinguished from transport. But then the theory of emission being rejected, the propagation of light not being a displacement of particles, one could not expect the speed of light in relation to a system to vary according to whether the latter is in 'repose' or in 'movement'. Why should it take account in an altogether human manner the perceiving and conceiving of things?
Let us place ourselves frankly within the hypothesis of reciprocity. We should now define, in a general manner, certain terms of which the meaning appeared to us to have been sufficiently indicated till now, in each particular case, by the very usage that we have made of it. We shall therefore call a 'system of reference' the tetrahedron of three right angles in relation with which it would be possible to situate, by indicating the respective distances from each face, all the points of the universe. The physicist who constructs a Science will be attached to this tetrahedron. The summit of this tetrahedron will generally serve him as an observatory. Necessarily the points of the system of reference will be at rest in relation to one another. But we have to add that in the hypothesis of Relativity the system of reference will be itself at rest during all the time when one would employ it for reference. That which constitutes the fixity of a tetrahedron in space, what could it be if not the property which one bestows on it, the momentarily privileged situation which one assures it, in adopting it as a system of reference? As long as one retains a stationary ether and absolute position, motionlessness for ever belongs purely and simply to those things; it does not depend upon our decision. Once the ether has disappeared together with any privileged system and fixed points, there is nothing but relative movements of some objects in relation to others; but because one cannot move in relation to oneself, the immobility will be, by definition, the state of the observatory where one places oneself through thought; there exactly is the tetrahedron of reference. Surely nothing would prohibit the supposition at a given moment that the system of reference is itself in movement. Physics has very often an interest in making it so and the theory of Relativity could fit itself without difficulty into this hypothesis. But when the physicist puts into movement his system of reference it means that he is choosing provisionally another system for reference which would then become immobile.
It is true that this second system could be put into motion by thought in its turn, without thought necessarily choosing its habitat in a third one. Then it oscillates between the two immobilizing them in turn by its comings and goings, which are so rapid that it could give itself the illusion of keeping both of them in motion, one as well as the other. It is in this precise sense that we shall speak of a 'system of reference'.
On the other hard we shall call an 'invariable system, or simply a 'system' all groups of points which conserve the same relative position and which are therefore immobile in respect of one another. The Earth is a system. Doubtless a multitude of displacements and changes show themselves at the surface and hide in the interior; but these movements take place within a fixed order: that is to say, that one could find on the face of the Earth as many fixed points as one could desire, each fixed in respect of the other, and relate oneself only to these. The events that would take place during the interval passing them to a state of simple representations will be nothing more than images, represented as paintings in themselves successively in the conscious ness of the motionless observers at these fixed points.
Now a 'system' could generally be erected as a system of reference. By that we should understand that it is possible to localize in the system, the system of reference which one has chosen. Sometimes it would be necessary to indicate the particular point of the system of reference which one has chosen. Sometimes it would be necessary to indicate the particular point of the system where one places the summit of the tetrahedron. Most often it would be useless. Thus the system called Earth when we consider its state of rest or movement, in relation to another system, could be envisaged by us as a simple material point: this point then becomes the summit of our tetrahedron.
Or else, once more giving to the Earth its dimension we shall suppose that the tetrahedron is placed wherever one likes to place it. From a 'system' to a 'system of reference' the transition is also continuous if one places oneself in the theory of Relativity. It is essential in effect for this theory to scatter on its 'system of reference' an indefinite number of time-pieces adjusted with one another and therefore also with the observers. The system of reference could not therefore be a simple tetrahedron containing a unique observer. I would also lay down that the 'time-pieces' or 'observers' have nothing of materiality; by 'time-piece' one means here an ideal registration of time according to determined laws or rules, and by 'observer' an ideal reader of the time that has been ideally recorded. It is no less true that we represent now the possibility of a material time-piece and living observers at all points of the system. The tendency to speak indifferently of a system or of a 'system of reference' was moreover immanent to the theory of Relativity from the beginning. Therefore it was by immobilizing the Earth, in taking this global system as a system of reference, that one explained the invariability of the result of the Michelson-Morley experiment. In the majority of cases the assimilation of the system of reference into a global system of this kind presents no inconvenience at all. And it could have great advantages for the philosopher who might seek to find to what measure the Times of Einstein are real Times, and who, because of this, will be obliged to post observers in bone and flesh, as conscious beings at all the points of the system of reference where there are 'time-pieces." (98)
Here we see how Bergson makes use of a tetrahedron at whose apex a universal physical observer is present. He distinguishes the rival claims of propagation and transportation and arrives at the possibility of thinking of the reciprocal movement of propagation along a vertical line wherein observer and the clocks observed would belong together at every point of the time axis. This is what Bergson would like, but relativists seem to prefer to put clocks and observers at every point of the tetrahedron. Bergsonian speculation excels itself here and the reader might have to go back to the words of Bergson in the fairly long quotation we have just cited in order to fully appreciate its workmanship. All we want to underline here is the correct schematization adopted by Bergson - that it is not unlike what we suggest ourselves.
Further on in the quotation to follow we find him bringing space and time more idealistically into close unity. Stating that time and space enter into homogeneous relationship only by the act of mixing, resulting from the movement of the two rival systems postulated by him, each alternately occupied by observers, Bergson says:
"That is to say he (the observer) would not know to abandon it (his system) without installing himself in another system: the latter which is thus at rest will have a Space and a Time clearly distinct in the same way as ours. In the same way as space could swallow up Time, and Time in its turn absorb Space, so are Space and Time always virtual and merely thought of, never actual and realized. It is true that the conception of such a Space-Time will act on the perception of actual Space and Time. Traversing Time and Space which we have always known to be distinct, and by that very reason as amorphous, we shall be able to see, as if by transparency, an organism of articulated Space-Time. The mathematical notation of these articulations, effected on a basis that is virtual and carried to its most high degree of generalization, will give us an unexpected hold on reality. We shall then have in our hands a powerful means of investigation, a principle of research of which one could predict even from the present, that the human spirit will not renounce it, even when experience should impose a new form to the Theory of Relativity." (99)
After presenting us with a structurally conceived visible organism as "a powerful means of investigation" he continues:
"To show how Time and Space do not begin to interlace except at the moment when either one or the other becomes fictitious, let us return to our system S' and our observer who placing himself effectively in S' transports himself in thought into another system of S, now immobilize it and suppose S' to be animated by all possible speeds, we wish to know what signifies in the Theory of Relativity the interlacing of Space and Time considered as additional dimensions. We shall be changing nothing in what results and we shall be simplifying our exposition in supposing the space in our systems S and S' is reduced into a unique dimension, to a straight line, and that the observer in S' having a vermicular form occupies a portion of this line." (100)
We see how the notion of a space-time continuum given by Minkowski has been subjected to a drastic epistemological revision in the light of the Absolutism that Bergson tacitly represents. Even the vestiges of the duality of space-like and time-like dimensions which both Einstein and Minkowski rely on, stand here fully abolished and revised in unitary terms.
Of the two structural images presented to us by Bergson, the former represents reality and incorporates features of modern phenomenological, 'topological,' or "projective" disciplines. Analysis in situ and analysis in terms of qualitative non-metric space are implied here, as also the idea of continuity and reciprocal one-to-one correspondence, which are essential features of projective geometry.
The second image represents pure becoming in terms of the vertical dimension of time within the scope of which space and time are represented as existing without any difference between them. With Bergson we have nearly come to the limits of permissible schematic speculation. If we take one step further we might be charged with being too fanciful. Although such a free fancy has been permitted by Einstein himself, we shall not take advantage of this concession but instead shall try, as far as possible, to manage without it.
28. A STRUCTURAL MODEL WITH ABSOLUTE STATUS ALREADY IN USE
Conics is a branch of geometry much favoured by ancient astronomers because of the various curves, shapes or lines accommodated within its scope of study. These features are particularly favourable in astrology and cosmology. The circle, parabola and ellipse can all easily be thought of in terms of conic sections. When two cones have their circular bases juxtaposed we have a structural model. Such a model is used nowadays by paint dealers who probably adopted this model primarily for reasons of utility and have taken to its use as if by chance in their efforts to link names with numbers or letters or other monomarks of a graded series referable to all possible colours distributed conveniently in space, with an intrinsic or absolute structure of its own.
The structures of space of both Lobachevsky and Riemann resulted from a similar search when Euclidian space was found to be inadequate. We know that the many varieties of geometry now in vogue in the mathematical world began with the epoch-making analytical geometry of which Descartes was the immortal founder. We have also referred to the law which states that progress in mathematical thought takes place by means of the workability or utility of certain innovations. Mathematics is based on axiomatic thinking, but as O.G. Sutton has pointed out, (see p.136 above) mathematicians are no respecters of tradition.
There are at present two interesting sets of geometry, one before and the other after the structure of space has been revised. The latter gives it a qualitative content without being rigidly confined within the axioms of the Elements of Euclid. The former, called Euclidian geometry is not however ruled out altogether, but finds its place as one instance among other geometries. Together they all form an independent whole fully formalized by Hilbert. That geometry is to be thought of in purely abstract qualitative terms and actual things, as particulars in life, as having a mere arithmetical status, must be strictly kept from prejudicing our thoughts here.
Euclidian geometry is an ancient discipline meant primarily for the purpose of measuring land and, as such, a paper and pencil suffice for its functioning. Now space can be thought of without metric ideas applying to it. Scalar or vectorial geometry gives place to more pure directed numbers where further qualitative liberalization in the form of tensorial ways of representing reality takes place. With projective space one thinks in terms of a situation and a surface helping us to fix them or analyze them in situ. Projective space brings in the idea of continuity and disparity together in the analysis of space with its one-to-one correspondence, between points understood as ensembles or groups, within its own abstract variety of space. All these emancipating factors have been operating in our times, justifying more and more a structural language, helping in the analysis or integration of all proper and improper elements.
All these features must be evident to the reader already from what we have said above. What we wish especially to underline here is that the utility and the workability or the vogue into which a certain structure has entered is in itself what makes it sufficiently interesting for us to adopt. This is particularly so when we are helplessly groping, as it were, for a convenient model to adopt at least as a working basis for the purposes of this study. We are referring here to a model now widely used by paint dealers for fixing the meaning of all kinds of possible colour variations.
Space has been conceived in qualitative terms in the structural model we have referred to just now. It is also sometimes called a colour solid.
How it is constituted has been described in detail by us already in the monograph devoted to a language for Unified Science (see the footnote on page 113, above). For ready reference, we are quoting from Webster's New International Dictionary (Second Edition, 1934):
"Colour may be regarded as a psychological category; it can be described and specified in terms derivable from introspective analysis, without any reference whatever to wavelengths, to energy, or to any physical category; but it is also possible to state the physical correlates of the psychologically determined attributes of color and to draw up certain psycho-physical relations between them. All colours are divisible into two classes, the chromatic colors, as reds, greens, purples, browns, and pinks, and the achromatic, or neutral, colors, including black, white, and the intermediate series of grays. The latter are found to differ from each other only in their degree of resemblance to or difference from black (or white). It is possible to form a series ranging from black to white, with a median gray at the center differing equally from black and white, and with each other, gray differing from its immediate neighbors by equal sense of differences. This series can be made into a scale by assigning an ordinal number to each gray, either ascending toward the lighter grays from black as zero or ascending with positive numbers and descending with negative numbers from median gray as zero. That attribute which thus measures the variation of the grays is called brilliance; dark grays have low, median gray has medium, and light grays have high brilliance. Chromatic colours differ from each other not only in brilliance, but also in hue and saturation. Hue is that attribute in respect to which colours may be described as red yellow, green, or blue, or as intermediate between two of these. Hues form a natural cyclic series (hue cycle, colour cycle, and colour gamut). Colours of the same hue and equal brilliance may differ from each other in saturation that is, in vividness of hue or in degree of difference from gray, In terms of these three attributes, colours may be arranged in a symbolic tri-dimensional space (colour solid) having the gray series as axis, with median gray at the center and black and white at the extremities (Fig. 1). Corresponding to each gray is a plane perpendicular to the axis, in which lie the points representing all colours of equal brilliance. In each plane, hue is represented cyclically in the order of the hue cycle, and saturation is represented radially, with the axial points (grays) as reference points of zero saturation. Thus any color can be specified by giving three ordinal numbers (colour constants or dimensions) which are coordinates of the corresponding point in the color solid. By the establishing of arbitrary division points on the scale of brilliance and saturation, any color can be described as having very low, low, medium high or very high position in these scales ...
By the establishing of arbitrary points of division on the hue cycle, hues can be classified as yellowish-red, reddish red-yellow, and red-yellow, yellowish red-yellow, reddish-yellow, yellow, greenish-yellow, yellowish yellow-green, etc. All principle definitions of colors in this Dictionary are in introspective terms like the following: "bay, a color, red-yellow in hue, of low saturation and low brilliance"; "carmine, a colour red in hue, of high saturation and low brilliance." (101)
An illustration of the structure described is to be found in file: COLOUR SOLID
For our purpose of a basic model, all the actual colours qualitatively brought into use in this colour solid need not be kept in mind. We are interested only in the pure relational aspects giving coherence to any natural group of specific qualitative factors. What applies to colour relations must apply also to sound qualities. The possible colours constitute the most concrete and natural of any such a groups. The model succeeding in relating them coherently and systematically at once, without any duality, as between percepts and concepts, will thus have a unique status of its own. Such a status can even be said to be absolute as we shall presently clarify. What works in the limited field of possible colours can be extrapolated and applied to other sets or qualities, in fields further and further removed indefinitely, and they can also be conversely thought of in terms of interpolation. This is permissible according to mathematical usage.
The possibility of extending the structure of the colour solid mentioned above to the appreciation of sets of values that enter in integrated fashion into human affairs, when these are pushed one step further into the domain of colour harmony and appreciation, is masterfully presented by Kant in his Observations on the Feeling of the Beautiful and Sublime (102). In this work we find him tacitly adopting the same frame of reference for bringing many items of value under this double heading.
There is a further and more important use of the same structural analysis which can be used in matching correctly corresponding words representing shades, tints, depths, saturations, hues, etc., as between German (as in Kant's case) and any other language. Value appreciations must necessarily have the same words or corresponding terms representing them in all dictionaries with an intrinsic or extrinsic one-to-one correspondence. Natural clusters or families of words that we have suggested elsewhere for a non-alphabetically conceived dictionary can more easily be admitted as practicable in the light of Kant's interesting work belonging to his pre-Critique period.
We have alluded to the absolutist status of this structure. This is already evident in the qualitative and highly abstract and wholesale, universal or general character of this structure which can refer to any or all bodies, big or small, at any time or at any point in the universe. One has only to place oneself sympathetically, as we have said before, at the core of the situation required by both Vedantic and Bergsonian. metaphysics.
The top limit will supplement the bottom limit by gentle gradations without vertical contradiction, but with a pure continuity at its core. At the grey point at the centre between the two poles of the vertical axis there is the meeting of space and time factors fully articulated and referring to perceptual an conceptual factors of physics and metaphysics respectively. Paradox, which is what hides the full view of the Absolute can thus be structurally analyzed and by this very act made to fall, revealing the fully absolutist status represented by the central point of origin of both the visible and invisible aspects of truth at once.
Each cone has a third dimension facing opposite ways from the point of origin and extending upward into the world of the Logos, and downward into the world of the Nous. The double world of two dictionaries made up of concepts and their corresponding percepts is thus fully covered. Colour space reveals the character of this third dimension sufficiently. The following description of the colour solid by W.M. Judd, found in Collier's Encyclopedia, is fully explanatory of this matter:
"Colour harmony results from the juxtaposition of colours which are selected according to an orderly plan which can be recognized and emotionally appreciated. Application of this principle requires a consideration of uniformly scaled colour space: a tri-dimensional array of points, one for each color, so arranged that equally contrasting colour pairs are separated by pairs of points equally distant. The vertical dimension of color space is lightness; hue is represented by an angle about the central vertical axis (black through gray to white), and saturation by distance from any regular path in the color solid constituting an orderly selection, and, particularly if chosen at regular spacings along this path, may be quite harmonious." (103)
Colour harmony and other relationships can all be thought of together with the help of this model. It is also possible to think of groups or families of other concepts or percepts into which all words, in any dictionary can be arranged as antonym and synonym trees, facing both ways like twin structures after the model named after Porphyry.
Actual practice has to work out further the details of this new kind of double dictionary, non-alphabetical but more organically conceived, which is possible in any language. This has already been partially adopted in both the Sanskrit Amarakosha and in Roget's Thesaurus. It is interesting to note that in the Svetasvatara Upanishad (17, I) we also find a similar reference to something resembling a colour solid:
"The One who, himself without colour, by the manifold application of his power (sakti-yaga) distributes many colours in his hidden purpose, and into whom, its end and its beginning, the whole world dissolves - He is God (deva)!
May He endow us with clear intellect!" (104)
Here our aim is to show how physics and metaphysics can have a common two-sided structural model. As long as the colour solid model serves us adequately for all our purposes of unifying and integrating linguistic elements, so as to fix their connotations or denotations with certitude, we have no valid reason to disadopt this model, waiting as it were like a foundling child to be adopted. Since the world of the dictionary normally covers all concepts with their corresponding percepts which might interest any group of human beings at any given time, this colour solid may be considered as covering the whole of significant human discourse anywhere at any time.
29. THE GREAT POSSIBILITIES OF INTER-DISCIPLINARY STRUCTURALISM
Just as colour clashes and lack of harmony can be avoided and a healthy perspective maintained through the colour solid, so we can think of all the varieties of human interests within the global world of discourse or total knowledge situation in which all persons find themselves situated. Invisible frontiers between human beings are set up by closed and static loyalties to lopsided interests extenuating, exaggerating or distorting one structural aspect at the expense of another. These frontiers, each with its own ideology, tend to disperse humanity by fragmentation and partitioning due to over-specialization whether in science or in the domain of more general ideas. Much vain verbosity fills libraries propounding the claims of rival interests.
When this is unitively understood the individual can learn to place himself sympathetically and without clash of interests in the value world to which other fellow humans might belong at any given time. He has to learn to enter into a unitive situation equating the Self to its own non-Self counterpart. What we call human progress must take place by physics and metaphysics going forward hand in hand and not one at the expense of the other. Such are some of the general ethical considerations that come to mind when we think of the possibilities of recognizing the structural unity between two disciplines, however apparently remote they might be from each other.
All maxims meant for human welfare such as "loving one's neighbour as oneself" stem out of the necessity for humans to understand one another across the linguistic and cultural frontiers of custom, ideology, politics, etc.
Here again we have to stress the importance of entering inside the situation before passing judgment about its value. Each person lives at the core of his own structural unit of value and thus inwardly viewed he can claim the same attention as any other. From domestic frontiers to the clash of national interests the same principle of inequality due to wrong thinking must be recognized. An integrated, unitary and absolutist approach to all possible values natural to humanity, understood as a part of the Science of the Absolute, can alone help in correcting the consequent disasters due to such unscientific thinking.
There is also a compensatory factor to which full allowances have to be made. Between realism and idealism man can identify himself vis-a-vis philosophical or religious values, and closed or open loyalties, by choosing his own position on a graded scale of values distributed along a vertical axis within the structural system proper to him. A compensatory factor becomes operative here. What is gained on the negative side is lost on the positive or vice versa. Orthodoxies and heterodoxies can take their positions in such a compensatory scale of values. The principle of equality can then become evident when the constant and resultant totality is given its due importance. Thus the recognition of the overall and double structure in the world of values tends to bring mankind together and promote human solidarity and understanding. (105)
The elements of such an understanding are not without some recognition even at the present time. A king who stands among the members of his own bodyguard dressed in the same uniform, say for a photograph, still has a distinct vertical dimension in the mind of each of his guards, while their own status remains pluralistic and horizontal. He resembles a bird which is more important than its cage. In the observance of the protocol between two completely independent states in determining the order of precedence, one can sometimes see this kind of absolutist structure kept in mind. National flags are given absolutist status within their own frontiers. Each nation is said to have its own legal personality independent of its area or population. Even the petty ruler has guns fired in his honour while a business magnate financially worth ten times more is only a common citizen. In the world of ecclesiastics the same recognition of absolutist structural unity is respected more familiarly.
When the ruler is a president there are certain absolute privileges or immunities enjoyed by him, even in the most thorough-going of modern democracies. All these tend to show that the absolutist way of treating one's neighbour is not something new even in the most modern set-up.
Wreaths are placed at the graves of national heroes by visiting dignitaries, although such an action is highly reminiscent of ancestor worship. All this might be considered outmoded hereafter by modern men. We have referred to these instances only to point out that what interests us in this present work is nothing new. We here plead only for a more open and scientific recognition of such features.
When we think of the world of ideologies instead of that of politics, we can give several examples. Existentialism refers to a current vogue in the world of ideologies. Many books have been written on this subject, some of which are still within the pale of Christian thought, while others are uncompromisingly sceptical and even atheistic. The varieties of existentialism, whether orthodox or heterodox, may have many divisions, but they are all recognizable as presenting a common front against all those who belong structurally to the side of essence rather than existence. Essence and existence therefore must belong to opposite poles in the minds of these rival groups. This is a structural secret which should be kept in mind by the reader who is obliged to wade through a large variety of arguments and counter-arguments between these schools of thought. Doing this helps him to appraise the overall nature of the chief bone of contention between them.
The same holds true if we take the rivalry, exaggerated and distorted out of all proportion in modern times, between democracy and communism; although from their dictionary meanings no great disparity intervenes between the ideologies behind these terms. This is because horizontal interests prevail over the vertical. Atheists and believers can be fixed into this same absolutist context, as also what is nicknamed "the free world" and its opposite imagined as existing behind some iron curtain or the like. Overall structuralism helps to abolish many of these frontiers. Besides helping in the course of human solidarity there are other perhaps vaguer advantages of structuralism such as its potency, power or beauty as an "instrument of future research" referred to already by Bergson. Greek drama, by respecting the three unities of time, place and action only recognized this same structural way with such advantage in its great tragedies. (106)
It becomes evident that structuralism is an all-important matter to respect even in everyday abstract thinking. When we say for example, that a heavy man sat on an abstract chair this structure is violated. The fourfold epistemological distinction implied in the principle of the quaternion in the heart of reality is not respected here. The Mandukya Upanishad also recognized these fourfold structural features.
To take another example from India, we believe that without the aid of structuralism, the intricacies found in works like Sankara's Bhashya (commentary) on the Brahma Sutras cannot be even approximately followed. On this point of structuralism found in Indian philosophy, the reader is referred to the author's translation and commentary of the Bhagavad Gita (107) where this subject is gone into in great detail.
If a professor speaking of Plato's theory of art compares it with Aristotle's theory, showing how the first is an "imitation of an imitation" and the second is just an "imitation of Nature", this distinction with all its implications will not be clear to his students unless they have a common frame of reference into which both these theories can be fitted. Likewise notions such as the 'general good' and-the 'good for all' cannot be clearly distinguished without a similar frame of reference, whether in ethics or economics. The surplus-value theory of Marx is also another troublesome matter to clarify. (108) Even in a subject such as semantics "syntactics" and "semiosis" involve the same horizontal and vertical correlation.
An actual, virtual, conceptual or nominal chair with four persons of corresponding status, who can only sit on the appropriate chair and thus not violate the epistemology involved, is the essence of the same structuralism we have tried to outline. If an actual heavy man "sits" on a nominalistic chair, the resultant situation can only be at best considered a joke or an absurdity. Eddington has written something along these lines, as follows:
"Let us first notice that the phrase "chairs we sit upon" adds nothing to the term "chair". For what sits on the chair is the body; and if we have to discriminate the scientific chair, i.e. the object, not really a chair, which the physicist describes, from the familiar chair, we must also discriminate the scientific body, i.e. the object, not really a body, which the physicist describes, from the familiar body. So when we sit on chairs the familiar body sits on a familiar chair, and the scientific body sits on a scientific chair. And if there is an abstract body it doubtless performs an abstraction of sitting on an abstract chair." (109)
The fourfold structure has thus to be respected at every step in common life if absurd situations or major disasters are to be avoided. The structural value world to which a wife naturally belongs has to be abstracted and understood by the husband if they are to have a happy marriage. (110)
Structuralism thus enters into everyday life in ways too numerous to mention, helping us both to live and let live.
To sum up, the greatest scientific validity or use of structuralism consists in the fact that when recognized as necessarily underlying different disciplines of human knowledge it can unite all of them as a Science of all Sciences with a common methodology, epistemology and axiology, belonging to all or each of them at once. The plan of the present work when further explained will reveal this important principle.
Before going into details of the plan of this work it would not be out of place here to sum up the position envisaged by a representative man of science in respect of the Universe and human progress in general. Instead of attempting to state this in our own words we have a more authoritative estimate from the pen of a contemporary front rank scientific thinker.
According to Werner Heisenberg the Sciences of Nature are to be looked upon "as parts of reciprocal actions between nature and man" (Cf. Chapter III: "Nature in Contemporary Physics", Gallimard, Paris). This German Nobel prize laureate in Physics, responsible for his famous principles of 1. Indeterminism in 1927 and of 2. "the Unitary theory of particles" generalizing cause and effect, said that at each instant the Universe chooses between all that is possible - and the most simple of the possible.
In his article in "Planète" (Paris, 1962) he wrote (our translation): "For the first time in the course of history, man finds himself alone with himself.,' (p.24).
Hitherto the Science of nature interested itself in an objective world to which man had to adapt himself. Today we live in a world totally transformed by man. For the natural sciences, "the subject of research is no more nature as such, but nature as given to human interrogation and to this extent man, again, does not face here anything but himself." (p.25) Further, Heisenberg points out that in science it is important to see the "cohesion of the 'great ensemble' (wholesale totality) and details only help to enhance the vision of the whole." In the course of the developments which took place during the last fifty years .... the aim has always been the same: the "Grand ensemble of natural laws" (p.26)
Regarding the scientific validity of "conceptual-systems" which have been elaborated especially in the science of electricity, he underlines their universal scientific validity as follows:
"The term "definite" as applied to the exact sciences of nature, signifies evidently therefore that there exist systems of concepts and of laws which from a closed totality and which are mathematically capable of formulation; it is valid for certain domains of experience; for these domains they have a universal validity and are susceptible neither to transformations nor modifications." (p.26)
However, Heisenberg adds further that there is an internal contradiction and an "auto-illusion" involved in the faith of certain scientists who say that there is here a "knowledge founded on science rather than on faith."
He states the enigma involved boldly, and the paradox is fully confronted by him when he writes:
"This signifies that the image of the Universe according to the Sciences of Nature ceases to be, properly speaking, the image of the Universe according to the Sciences of Nature."
Heisenberg sums up the blind alley which faces modern man as follows:
"We find ourselves firstly alone with ourselves. The hope of a progress that is sure by means of the increase of man's material and spiritual power finds within the situation itself a limit, although only a glimpse of it is given to us; the dangers are at least as great as the wave of optimism which it draws behind it, to believe that this progress would break itself forcefully on this limit. By this apparently unlimited growth of material power, humanity finds itself in the situation of a captain whose boat is constructed with such a great quantity of steel and iron that the turning of his compass instead of indicating the north, does not orient itself except towards the mass of iron of the boat." (p.27)
Although relying on an analogy, Heisenberg is not without a knowledge of the two-fold structural implications of space here as seen from his concluding words:
"The space in which man develops himself as a spiritual being has more dimensions than that in which alone during the last centuries his activity has been deployed." (p.27)
30. THE PLAN OF THIS WORK
No science can give full certitude without a normative reference properly belonging to it. In the preliminary remarks our aim was to convince the modern scientifically-minded person that the integration of all physical and metaphysical disciplines can be accomplished through the principle of the Absolute as a Norm.
The Absolute is not an empty word nor a mere mathematical abstraction. With an axiomatic status where the a priori normally resides, it has to have a concrete universal content if it is to be fully scientific in both an outer experimental and operational sense. It needs as well an intuitive sense based on the inner experience of the bold and correct speculation to be found in the context of the perennial wisdom of both the East and the West.
To give this normative notion a content, we have laboured in the foregoing sections to explore possibilities in the domains of modern knowledge, including even the world of machines. We hope we have more or less succeeded in convincing the reader about a certain structuralism found acceptable even to the latest modern thinkers. Structuralism helps us to establish a link between disciplines seeming to differ radically.
It also helps us to find a means of integrating, at least for purposes of easy communicability, whether for comparison or contrast, a propos aspects of truth-value within each of the major disciplines. Even within the scope or amplitude of any individual discipline, structuralism comes in handy in bringing all diverse factors into a unified whole both for integration as well as for critical analysis. It is not irrelevant therefore for Bergson to refer to such an "Instrument" (see page 154 above), as being full of potent possibilities for human beings forever. He means to say, in other words, that when structuralism is correctly understood it can have a fully absolutist status, yielding a frame of reference or a basic form of thought round which a veritable Science of Sciences can be built. Because of the importance of clarifying the implications of such a normative schematic structuralism in order to give a fully scientific status to our own work, we have indulged in this rather long-drawn-out introduction which we hope the reader will pardon.
It now remains for us to let the reader peep behind the curtain as it were, so as to reveal to him an advance view of the plan of this work. In reconstructing both modern material available in the West and the rich treasures forming the heritage of the wisdom of the East, we hope to bring them together unitively and integrally, yielding at least for our present purposes, although perhaps not finally, a Science of the Absolute.
We have necessarily to approach the subject, as it were, from two opposing poles of the total situation.
The Vedanta of India with its textbooks such as the Bhagavad Gita and the large body of literature called the Upanishads, as we have already stated, claims to be a Science of the Absolute called Brahma-Vidya. It is a mistake commonly made to treat this part of wisdom literature as belonging to Hindu religion. By its dynamic and open outlook such literature refuses to be fitted into the orthodox context of a closed and static religious set-up. Be this as it may, we on our part are going to look upon this body of Vedantic learning as a sastra or science. Such a status can be claimed for this literature and clearly proves itself from the colophon found at the end of each chapter in the Bhagavad Gita (111). In our own commentary on this book we have tried to justify this claim made by the ancient authors themselves. (112)
When we think of the West similar absolutist wisdom exists, even in the context of what people like Bertrand Russell have begun to call "The Wisdom of the West." Because of the divorce of philosophy and religion, due to tragic historical circumstances, such wisdom is less evident because of its compact compartmentalization.
Thus science, metaphysics and theology took different paths and the elements of absolutist wisdom were distributed within these three domains. They must all be gathered together before the main currents of what is known already as perennial philosophy can be harmoniously thought of. Included in this will be the great contributions of both Christian and non-Christian mysticism.
Science itself, in its most modern developments, tends to support wholesale wisdom, rather than piecemeal trial-and-error methods of annexing small territories of truth into its body. Science is undergoing a drastic epistemological and methodological revision. It is tending to include into its corporate body branches of knowledge like ethics and aesthetics which depend upon judgments of value. In doing this it is possible for science to attain to a status of a body of knowledge fit to be included alongside the wisdom literature of the world. When this is done we will have a complete Science of the Absolute. Such a science will have an epistemology, methodology and axiology of its own, treating of existential, subsistential and value factors at once. The question of scepticism or belief will not arise at all when Unified Science becomes fully normalized. As against this kind of condensation, on the part of the West, of a large body of scientific knowledge into an integrated whole, we have had in India, a complementary tendency in which apparently diffuse or subtle speculation had been put in correct, though somewhat crypto-crystalline form.
The authors of the various sutras (aphoristic strings or threads) belonging to the six main darsanas (visions of truth in the absolutist context), are seen to be fully conscious of the structural implications of the totality of what each had to say. The mystical language of the Vedas and the Upanishads also contains crypto-crystalline elements of a protolinguistic order, which enables them to be treated in a precise way, whether by the original founders of the schools of philosophy or by their later revaluators. One is able to discern in the vast body of literature belonging to the study of the notion of the Absolute, elements to which the authors definitely gave a scientific form and precision in order to formulate what they wanted, vaguely at first, to express. In the light of the structuralism examined in our foregoing sections it will not be wrong for us to assume that this particular synthetic and a priori approach implied in Vedantic wisdom confers on it a fully valid scientific character. If mathematics can be considered a science in which one aspect of it brings certitude to the other, as we have pointed out in the example of the Pythagorean theorem, it would not be considered far-fetched to think that the kind of certitude found in Vedanta where the a priori and the a posteriori go hand in hand, can give the same kind of resultant certitude. This must be sufficiently clear from what we have said already. Thus it is safe to assume that in Vedanta we do have before us for guidance a Science of the Absolute although sometimes presented in a rather amorphous or crypto-crystalline form.
In the hands of master minds like Sankara, Ramanuja, and Madhva, it can even be asserted that the unitive and structural elements have tended to become coherent even in a more or less crystalline form. (113) Some writers on Vedanta who can safely be assumed to be followers of Sankara, if not Sankara himself, have all attempted to consolidate and present to us a whole series of darsanas, keeping in mind a common methodology and epistemology. The Bhagavad Gita is an example of a work which attempts to present a series of points of view normalized under the dominant notion of the Absolute. The Sarva-Darsana-Samgraha (Epitome of all visions of truth) of Madhavacharya (114) represents a valuable work on. such comparative lines covering a series of sixteen different darsanas beginning with the Charvaka (Materialist) view of truth and ending with the Advaita Vedanta of Sankara which he does not cover in the Sarva-Darsana-Samgraha, but instead refers the reader to his other writings on this philosophy.
There is still another extant work, which does not however rise to the same degree of respectability in our estimation, attributed popularly to Sankara and entitled: Sarva-Darsana-Siddhanta-Sara-Samgraha (Epitome of all Essential Finalized Doctrinal Visions of Truth), which is on the same lines.
The desire to present the whole range of wisdom as one unified body of knowledge is not only evident here but can even be noticed in the Western context in such works as Aristotle's Organon and Francis Bacon's Novum Organum. Plato and Fichte also may be credited with attempting some such integration. (115) Such attempts however are mostly unsatisfactory or inadequate from a fully scientific standpoint. Thus the common schematic element showing itself through a linguistic or semantic medium comes into the picture as a new integrating factor, at once making not only Vedanta but also modern science, important, because it shows the way to the possibility of a fully unified Science of the Absolute.
The two kinds of certitude that have flourished from opposite poles as it were, of the total situation implicit inhuman understanding, have had their own proper growth, each with their different backgrounds; the one tending to exclude belief and the other tending towards it. Together they reveal how, in one and the same normalized discipline what is 'positive' certitude on the side of physics and what is 'negative' in metaphysics can meet in a central certitude that is apodictic. These two certitudes can fuse into one fact, truth or value. The various attempts, especially of sages in India, to bring different visions of truth under the same normative reference, have contributed much in the form of overall laws regulating correct speculation. They have only to be restated here correctly.
Such evidences are scattered all over in the great commentaries (bhashyas) of the teachers (acharyas), and when collected and ordered they manifest a firm basis desirable for the Science contemplated by us here. Besides the commentaries themselves there have been prakarana-sastras (compendiums containing definitions, etc.) such as Sankara's Viveka-Cudamani (Crest Jewel of Discrimination) which give more formal finality to the notion of the Absolute. Although later works on similar lines have sometimes become overladen with scholastic elements of a polemical hair-splitting order, we have at present sufficiently stable ground on which to stand. About 1000 years after Sankara, when much polemical or scholastic elements had confused the issues, there came the contribution of Narayana Guru.
At this point it is necessary to explain the nature of the bi-polar vertical affiliation of a sishya (disciple) to a Guru (spiritual teacher), as the present writer happens to be a disciple of Narayana Guru. Such a bi-polar affiliation should always be understood as properly belonging to the context of the wisdom of the Absolute, without any merely arithmetical and extraneous implications attached to it. Sankara has explained this pure relationship in the very first verse of his Viveka-Cudamani where he paradoxically refers to his own guru, as visible only to the trained eye of the knower of Vedanta, and invisible to those without such knowledge. (116) We have also elsewhere in our writings fully explained the nature of this time- honoured way of affiliation in the vertical, hierarchical succession (parampara) of a chain, as it were, of teacher-disciple links, which alone guarantees, anywhere and at anytime, the preservation of this highly subtle kind of teaching. (117) Here it is necessary to point out also that this relationship is being further purified by us in an open and fully critical and scientific spirit, any traditional philosophical or religious implication. No personal prejudice in favour of one's own Guru should here be presupposed.
This affiliation is wholly absolutist in character. The torch of wisdom passes best across generations through the personal medium of vertical succession of teacher and pupil.
It can be boldly asserted, even in the beginning, that in the Darsana Mala (A Garland of Visions of the Absolute) Narayana Guru has, in the context of human understanding treated as a whole, for the first time been able to string together all the points of view natural or possible into a veritable "Garland of Visions of the Absolute" as the title itself claims.
Philosophy or science is inevitably obliged to take its stand on a series of possible positions or grounds, which can be imagined in practical life to range between the fully realistic and the ultimately idealistic. The total knowledge-situation has its own global world of discourse having a structural ambivalence or polarity between what is merely physical and what is metaphysical, when the mind or the spirit places itself in a more idealistic position. Although these two antinomian poles tend to divide the subject dichotomously into two halves, we have to use our imagination here so that we can bring into dynamic interplay the ambivalent factors involved in the overall principle of compensation, which holds good along the whole vertical amplitude within the limits of which all thought or speculation must necessarily oscillate. We have to concede this in the name of the structure of the dynamism which we have explained already.
To visualize the same more clearly, let us think of a perfect crystalline quartz of a regular symmetrical shape, not necessarily chromatically coloured, but merely smoky in its bottom half and clear in its top half. The smoky and the clear halves are to be imagined as mixing in imperceptible gradations from both the extremities of the crystalline axis passing through its solid centre. We should then imagine this crystal as moving from the bottom to the top in an overall knowledge-situation. When it is at the bottom of such an imaginary scale the whole crystal is pervaded by smokiness with the bottom pole doubly so, making it splendid, as it were, by its absolute darkness. When raised slowly through intermediate gradations one should imagine the step-by-step encroachment of the clarity or full brightness at the opposite pole, reducing thereby the full negative blackness at the bottom pole as it rises to the zero point of origin at the centre between the two extremes. Here smokiness and non-smokiness cancel each other out into a neutral intermediate tint or shade. We can supply the remainder of the working of the principle of compensation if this crystal is further raised to the top.
Physics and metaphysics interlace intimately in a similar compensatory bi-polar fashion giving us the possibility of any number of intermediate positions, where one or the other of the factors involved is dominant or recessive. When both are balanced we get a normalized neutral position where physics and metaphysics embrace each other in full equality of status.
This position functions as the normalizing reference for all others, whether on the plus or minus side of the axis. Such a detailed structural analogy must necessarily be kept in mind because of the principle of reciprocal compensation involved in unitively treating points of view possible in the context of the Absolute, without falling into the error of treating physics or metaphysics disjunctly, which if adopted, will altogether spoil the game of normalized scientific speculation.
The experimental world is dependent on description, i.e. on the world of discourse, while metaphysics is dependent on the non-experimental, where inner experience takes over from what the hands of the experimenters have laid bare. Eddington makes this interesting point between what he calls theory and observation:
"A distinction is commonly made between observational and theoretical knowledge; but in practice the terms are used so loosely as to deprive the classification of all real significance. The whole development of physical science has been a process of combining theory and observation; and in general every item of physical knowledge - or at least every item to which attention is ordinarily directed - has an observational and partly theoretical basis." (118)
The perceptual and the conceptual when normalized in the light of the schematismus of Kant adhere to each other without any cleavage of duality between them. The colourful chromatic world which we might want to relate with this basic achromatic structure will have shades or tints corresponding to dark or light, saturated or thin with bright or dim lines belonging to any number of grades of the colours of the spectrum, according to the same compensatory principle as this structure occupies at various levels in the vertical axis.
The ten points of view that have been strung together into a garland by Narayana Guru belong each to a methodological, epistemological and axiological position of its own. This is intended by him when all ten such positions have been dealt with in symmetrical order. The Garland as a whole is meant to cover the whole range of possible positions. In each the central normative model is fully respected, giving it scientific clarity and position. Each vision proves itself by conforming to an overall structural scheme. The more one analytically or synthetically scrutinizes the series of verses, the more one discovers how there is a self-consistency and correctness in the various technical terms used by the correct Vedantins who have been his forerunners in formulating, perhaps in a more discursive way, the same Science. Here it might be opportune to point out that Sankara, whose name towers over all others and who stood for pure Vedanta, was himself conscious of these same structural requirements. This is revealed in his commentary on the Brahma Sutras where we find the following striking sentence:
"And that all the Vedanta-texts advocate the same view as to an intelligent cause of the world, greatly strengthens their claim to be considered a means of right knowledge, just as the corresponding claims of the senses are strengthened by their giving us information of a uniform character regarding colour and the like." (119)
The reference to colour as having a uniform character cannot be understood except in the light of the same structuralism that we stand for. Whitehead has this interesting remark to make about its character:
"A colour is eternal. It haunts time like a spirit. It comes and it goes. But where it comes, it is the same colour. It neither survives nor does it live. It appears when it is wanted." (120)
The Vedanta texts agree in giving us uniform directions or rules for speculation, descending, as it were, from the pole above, while perceptual factors, when understood in uniform and universally revised schematic terms, meet the descending dialectics by ascending, as it were, from the world of ontological realities. The a priori evidence of the word thus meets its own counterpart originating from the a posteriori. Both fuse and give a central, neutral, absolute certitude.
It is true that Narayana Guru gives one distinguishing name to each vision or chapter in the Darsana Mala, but these names are incidental and on final analysis change nothing of the absolutist content in terms of the value of each position taken. As in a parallelogram of forces, it is the equilibrium that counts. Whatever the duality involved, it is resolved in terms of the same equilibrium by the principle of compensation. Thus he should be taken as treating of the same Absolute, whatever chapter we might be reading at any given time. The name of the chapter is to be treated as a label only. This way of looking at the subject matter is nothing new, for it is also known in the Socratic tradition, The Good, the True and the Beautiful are treated as fundamentally the same. Keats also underlines this verity in the opening lines of "Endymion":
"A thing of beauty is a joy for ever: its loveliness increases; it will never pass into nothingness ...."
Further implications of the inner and outer consistency respected by Narayana Guru in composing the ten chapters, each of ten verses, forming the garland revealing the secret of the Absolute, will be clarified at the proper places in the present work. Suffice it to say here that from realism to idealism each of the ten chapters represents a tenable and representative philosophical or scientific position to each of which various subdivisions of schools can be imagined to belong.
Thus cosmology, theology, empiricism and positivism can all be thought of together in the first chapter, which starts by the supposition that the objective world has a reality of its own. Every other chapter similarly covers or answers to positions known to Western philosophy.
We shall explain the implications as we go along. Methodology, Phenomenology, Negativity and Normalization cover the chapters following the first, which can be called Empiricism or just plain Cosmology. The sixth chapter roughly covers all aspects of Instrumentalism, itself an offshoot of Pragmatism as known in the West. The seventh chapter covers Reason while the last three chapters where the accent is on axiological interests cover Devotion, Contemplation and Absorption. The present work while incorporating the translation from the original Sanskrit with our commentary fully respects and is largely indebted to Narayana Guru. The Darsana Mala is conceived with such perfect symmetry between each of its chapters, as also within each chapter itself, that when it is thought of as a whole it has such a self-consistency at every stage that the question of proof does not arise. Each vision or darsana results from the meeting of the a priori and the a posteriori, wherein outer experiment neutralizes inner experience, and as such yields both dialectical as well as apodictic certitude at each stage. When the Garland is thought of as a whole the reader will be able to recognize how the string from opposite sides meets at the top or behind at the back of the wearer.
At the most central point of the work (the conclusion of the 50th verse) is found one of the most famous of the great dicta or mahavakyas of the Vedanta: sat-eva-tat or "That verily is Existent." This hangs as a secret pendant, representing an extra jewel referring to the overall unity of the garland.
The maximum richness of certitude is meant by Narayana Guru to reside at this central position. Similarly, where the ends of the string meet at the back, we have to think on the one side of the epistemological status of a child who wonderingly and passively takes notice of the world around it, while at the other side in the very last verse the position is reversed and we have to think of a man ready to leave all worldly interests in favour of something of more interest-value to him beyond, in the form of an ultimate inner experience. These two opposite ends of the string have to be tied together to make the complete epistemological, methodological and axiological circle. Within the scope of this circle Narayana Guru has admirably succeeded in giving symmetrically conceived equidistant positions to all the philosophical views in the six systems of Indian philosophy. These systems are really six visions of Truth known as sad-darsana, whose contents have been here melted and reformed into the ten revised visions of truth found in the Darsana Mala.
A student of Western philosophy, sufficiently familiar with the broad groups into which modern thought can be made to fall, can similarly pass in review all modern philosophical visions of truth.
He can move from the one giving primacy to the perceptible, to the one referring to the subtlest of invisible axiological inner factors of experience. When this total amplitude is kept in mind the present writer wishes to relate the basic framework of the Darsana Mala to the large body of modern knowledge which, when revalued and restated in the light of the notion of the Absolute, will find its place side by side with it, and so be capable of being erected as a superstructure on the same foundations.
It requires a master architect to lay such foundations securely and correctly. It is a comparatively easy task to erect an imposing superstructure on it.
All modern scientific knowledge, whether gained through the Mount Palomar 200-inch telescope or the most powerful of sub-electronic microscopes, has some value in respect of the Absolute reality in which everyone is, or ought to be, interested. Here the West undoubtedly scores over the contemplative East. There is however, the opposite pole to the inspection through instruments applied to the outgoing senses, which belongs to introspection. In this latter discipline, where the eyes are withdrawn inwards, the East has always led the way from ancient times. The Science of the Absolute, as we conceive it in the present work, has to respect these reciprocal positions equally. Thus it is that we have to think of presenting the verses of Narayana Guru embellished and elaborated on the one hand with all that is precious in modern scientific progress, while on the other hand trying to preserve equally the ancient heritage of the wisdom of the East, as found in the Upanishads, Brahma Sutras and Bhagavad Gita, as well as the great philosophical traditions of both Buddhism, Taoism and all others. This will be our excuse therefore in the plan of the present work which is meant to have Brahma Vidya as its nucleus but which also tries to relate to it all significant modern knowledge consistent with the subject-matter, so as to present a sufficiently attractive edifice representing a wisdom free from geographical and traditional frontiers.
For purposes of convenience the chapters of the Darsana Mala can be divided into four parts, so that our introductions to them may not become artificially cut up, either making it necessary to repeat what was once said or making some boundaries overlap. The first three chapters can be considered as forming one group where the attention of the reader is still directed outwards to the objective, or at least, to the phenomenological world about us. The last three chapters, on the other hand, have an axiological unity of content between them. They belong strictly to the mystical rather than to the scientific approach. As to the four chapters remaining, which are more or less logical or psychological, referring centrally to consciousness as understood with its innermost implications, we can again think of a subdivision, as between the fourth and fifth chapters on the one hand, and the sixth and seventh on the other. These also have an inner symmetry between them. The fourth examines the overall possibility of negative error in the context of the neutral Absolute while the seventh proposes to overcome error positively through the training of the reasoning will, thus leaving error behind.
Further methodological or epistemological implications of these chapters will become evident when we come to deal with them. For the present it suffices to remember that the two central chapters, the fifth and the sixth, cling close together, giving unity and continuity to the total knowledge-situation understood schematically or nominalistically.
Finally some modern philosophers of science like Eddington still show hesitation in giving full and equal importance to perceptual as well as conceptual aspects of what they call the Philosophy of Science. Einstein said "Observation is the final arbiter": Eddington also takes this unjust and asymmetrical position. He is conscious of this asymmetry and its evils when he writes: "The one-sidedness is due to our acceptance of observation, not theory, as the supreme Court of Appeal" (121) Later on in the same context he says that a complete metaphysic is to be excluded:
"But such knowledge is beyond the borders of physical sciences and therefore does not enter into the description of the world introduced in the formulation of physical knowledge." (122)
Elsewhere Eddington quotes from Bertrand Russell's "Introduction to Mathematical Philosophy" (1919) where Russell writes:
"In actual fact, however, if the hypotheses as stated were correct, the objective counterparts would form a world having the same structure as the phenomenal world .... In short, every proposition having a communicable significance must be true of both worlds or of neither; the only difference must lie in just that essence of individuality which always eludes words and baffles description, but which for that very reason is irrelevant to science." (123)
The hesitation on the part of philosophers of science to take a fully neutral position (even though Russell refers to himself as a "neutral monist") between the rival claims of physics and metaphysics is at present the only impediment to the emergence of a fully symmetrically conceived Science of Sciences. When this symmetrical position is understood and respected fully, the transition from the Philosophy of Physical Science such as Eddington conceives it, to the revised metaphysics which is its own counterpart on the plus side of the situation, will become natural and fully justified in an overall absolutist context. The sixth and seventh chapters of the Darsana Mala thus need a treatment of their own as distinct from the two preceding chapters, although both pairs have a logical or psychological status. They belong together to the epistemological region where mathematics and logic interpenetrate, both employing the same structural elements from opposite sides.
One more word about the treatment we are going to give to these various sub-divisions: we shall give due place in the beginning to modern scientific knowledge of an observational order, while trying to balance such knowledge with speculative observations so as to round them off and fit them into the overall context of the present work. In the second half, especially in what pertains to the last three chapters, Vedantic speculation will receive sufficient counter-balancing treatment as against the observational aspects emphasized in the beginning. Brahma Vidya or the Science of the Absolute as understood in the authoritative source books will be fully respected at the end.
The four intermediate chapters will represent the part of the work where the subtle transition between physics and metaphysics will take place.
This work will therefore be in two parts. The first half up to and inclusive of the 50th verse will constitute the object-matter of the Absolute, while the second part will constitute the subject-matter of the Absolute. The second part will also have an Introduction of its own. Since these Preliminaries cover both and more specifically cover the contents of the first part, no additional Introduction will be needed. It will be helpful for the reader to keep this plan in mind to avoid possible puzzlement as we go on developing the subject-matter or the object-matter of this work.
The reader will also easily see that in our treatment of each of the chapters we have, as a rule, sandwiched the text of the Guru and his intended comments between a Prologue, in which the mind of a modern reader is prepared first to understand the full import of the text quoted, and an Epilogue, in which more traditional lore is passed in review so as to lend support mainly from the side of Eastern Wisdom. These sections, however, are not to be treated as strictly watertight in their compartmentalization.
One more last direction to the general reader or student: the Prologue part of each chapter is meant to make it easy for the reader unfamiliar with the treatment of the subject-matter adopted by Narayana Guru in each chapter of Darsana Mala to follow the line of reasoning adopted and to relate it to trends and vogue in modern thinking. He is recommended to scrutinize the text initially before seriously trying to understand the relevancy of the topics discussed in the Prologue. Preferably, we could come back to it after a first perusal of it with the text.
 See M. White, "The Age of Analysis", New York: New American Library ed., 1956, pp. 13-21, (Chapter 1: "The Decline and Fall of the Absolute"), for details of this trend.
 Whittaker, "Eddington's Principle in the Philosophy of Science"; a lecture delivered 9 August 1951, Cambridge Univ. Press, 1951.
 Ayer says: "And as tautologies and empirical hypotheses form the entire class of significant propositions, we are justified in concluding that all metaphysical assertions are nonsensical." "Language, Truth and Logic", London: Victor Gollancz Ltd., 1954, p. l.
 E.Husserl, "A General Introduction to Pure Phenomenology", trans, W.R. Boyce Gibson, New York: Collier Books, 1962, pp 41-42.
 L. Barnett, "The Universe and Dr. Einstein", American Library ed., 1958, p.108. New York: New American Library ed., 1958, p.108.
 H. Bergson, "Matter and Memory", trans. N.M. Paul and W.S. Palmer, N.Y.: Doubleday and Co., 1959,pp.101-107.
 R. Descartes, "A Discourse on Method", trans. J. J.M. Dent, 1965, p.167, parenthetical words ours.
 See our article (of a series): "The Search for a Norm in Western Thought" (Chapter 2: 'The Characteristics of Modern Philosophy'), Values, Vol.II: no.4 (Jan.1966), p.113.
 See our article (of a series): "Vedanta Revalued and Restated" (.Chapter 2- 'Schematic Protolinguism in the Vedanta'), Values, Vol.10 no.1 (Oct. 1964), pp.965-372, 381-384.
 A. Einstein,'"Space, Ether and the Field in Physics," from: S. Commins and R. Linscott (ed.) "The Philosophers of Science", New York: Pocket Books Inc. ed., 1954; & Washington Square Press ed.1966, p.478.
 "A neutrino could travel through an iron sphere millions of times larger than the earth's orbit around the sun and experience only one interaction." B. Ivanov, "Contemporary Physics", p.13.
 "Harper Encyclopedia of Science", Harper and Row, 1963, p.1215.edit. Newman, New York.
 M. Planck, "The New Science", New York: Meridian Books ed 1959, pp.143,155.
 See the following three writings of ours for clarification: 1. "The Word of the Guru", Ernakulam, Cochin (S. India): Paico Publ., 2nd ed. 1968,pp.155-171; 2. "The Philosophy of the Divine Family of Siva", Values, Vol.2: no.9 (June 1957); and 3. "The Androgynous God of South India".
 P. Freedham, "Principles of Scientific Research", London: Pergamon Press, 1961, pp. 50-51.
 K. Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge". London: Routledge and Kegan Paul, 1963, p.318.
 V.E. Smith "The General Science of Nature", Milwaukee, Bruce Publ. Co., 1958, p.58.
 Freedham, pp.51-52 .
 For a full discussion of this subject, see our three articles: "Existence"; "Subsistence"; and "Value Dynamism". Values, Vol.4: nos. 8, 9, 10. (May, June, July 1959), resp.
 A,S. Eddington, "The Nature of the Physical World", London: J.M. Dent, 1935, Modern Library ed., P-323.
 L. Wittgenstein, "Tractatus Logico-Philosophicus", tr, D, Pears and B. McGuinness, New York, Humanities Press, 1961, P-47.
 L. Wittgenstein, "Tractatus Logico-Philosophicus", tr, D, Pears and B. McGuinness, New York, Humanities Press, 1961, P. 131.
 H.Bergson, "Creative Evolution", Random House, Everyman's ed., 1944. trans. A. Mitchell, New York.
 T. Heath (trans.), "The Thirteen Books of Euclid's Elements, Book One: Common Notions 1", Cambridge Univ. Press, 1926.
 E. Schrodinger, "My View of the World", Cambridge Univ. Press, P.10.
 Liebnitz, "The Monadology and other Philosophical Writings" trans. R. Latta, Oxford, 1941, pp.217-218.
 See H. Bergson, "An Introduction to Metaphysics", Hulme, New York: Liberal Arts Press, 1955, pp.49-62.
 Schrodinger, pp.20-21.
 W.C. Wright (trans.), London: W. Heinemann, 1959, "The Works of the Emperor Julian, Vol.II".
 H. Bergson, (1st ed.) 1959. "OEuvres", Paris. Presses Universitaires de France.
 A series of eleven articles in "Values", : Vol.11:no.3, Vol. 12 no.2 (Dec.1965 - Nov.1966).
 "Kant: La Raison Pratique, Textes choisis par Claude Khodoss", Paris: Presses Universitaires de France, 1959, p.241, our translation.
 H. Bergson, "Creative Evolution" pp. 331-332.
 For further clarification of this new structuralism being elaborated and discussed, see the following two sources: 1. M.A. Tonnelat, "La Structure de la Théorie du Champ Unifié d'Einstein", Paris: Gautier-Villa, 1959; and 2. P. Destouches-Fevrier," Théories Physiques", Paris: Presses Universitaires de France, 1951.
 H. Bergson, "La Pensee et le Mouvant", 1280, from "Oeuvres", pp.1279-1280, our translation.
 Bergson, Cr. Ev., P.389.
 Bergson, Cr. Ev., pp.535-340.
 B. Russell, "Mysticism and Logic", London: George Allen & Unwin, 1959, p.2 .
 J. Burnet, "Early Greek Philosophy", Books, 1960, p.52. New York, Meridian.
 See R.E. Hume (Trans.), "The Thirteen Principle Upanishads", Oxford Univ. Press, 1968, p.242.
 Dionysius the Areopagite, "On the Divine Names and the Mystical Theology", trans. C.E. Rolt, London: Macmillan, 1957, pp.62-63.
 Bergson, "La Pensee", "OEuvres", p.1302, our translation.
 Bergson, "La Pensee", pp.1302-1303,.our translation.
 Bergson, "La Pensee", p. 129, our translation.
 Narayana Guru refers to this ocean of change and becoming in the very first verse of his "Daiva Dasakam, A Prayer for Humanity", trans. from Malayalam by us, with our commentary. See Values, Vol.3: no.3 (Dee.1957). A later revised translation by us of this prayer can be found in the English Appendix to the Gurukulam Magazine, Vol.8: no.12 (March 1972
 H. Bergson, "Durée et Simultanéité", Paris: Librairie Felix Alean, 1922, pp.226-227, our translation.
 E.Kramer, (Connecticut):"The Mainstream of Mathematics", Greenwich Fawcett Publ., Premier Book ed., 1961, p.188.
 Adler, 1964, "Thinking Machines", New York: New American Library, pp.12-13.
 For an interesting detailed description of how the Black Box works in relation to the person in training, see: S. Beer, "Cybernetics and Management", London: English Univ.'s Press, 1959, P.123 ff.
 J. Jeans, "The New Background of Science", Cambridge Univ. Press, 1944, p.41.
 H. Bergson, "The Two Sources of Morality and Religion", Trans. R.A.Audra and Brereton, New York, Doubleday, Anchor Book ED., 1935, p.317.
 See C. Tresmontant, "Pierre Teilhard de Chardin, His Thought", Baltimore (Maryland): Helicon Press, 1959, pp.109-110.
 "Collier's Encyclopedia", New York: Collier's Publ., 1958,
 Ducrocq, "Logique Générale des Systèmes et des Effets", Paris: Dunod, 1960, p.284, our translation.
 S. Ullmann, "Language and Style", Oxford: Blackwell & Co., 1964, p.5.
 See the "Sarva-Darsana Samgraha" of Madhavacharya, trans. E.B Cowell and A.B. Gough, London: Kegan Paul, 1894, pp.203-220. Max. Muller, "Indian Philosophy", Vol.IV, Calcutta: Susil Gupta Ltd., 1952, p.45, writes the following about sphota: "Sphota is in fact the word before it had been analyzed into letters, the breaking forth of a whole and undivided utterance, such as Go, 'Cow´ . conveying a meaning which does not depend on any single letter nor any combination of them". Though from our own point of view the idea of such a sphota may seem unnecessary, we cannot help admiring the ingenuity of the ancient philosophers of India in inventing such a term, and in seeing difficulties which never attracted the attention of European philosophers.
 See. S. Ullmann, "The Principles of Semantics", Oxford: Blackwell & Co., 1957, p.319, where reference is made to the "hidden metaphysics" of language, referred to by B.L. Whorf in "Language, Thought and Reality", London; New York: 1956.
 See the two articles: L. Bloomfield, "Linguistic Aspects of Science"; and V.F.Lenzen, "Procedures of Empirical Science," from: "International Encyclopedia of Unified Science", Univ. of Chicago Press, 1955, pp.215-276 and 279-339, resp.
 Nataraja Guru, "A Scheme of Integration of Elements of Thought, in view of a Language of Unified Science, submitted in French: ("Un Schema d'Integration des Elements de la Pensee, en vue de 1'elaboration d'un langage pour la Science Unifiee") to the Académie Royale de Belgique, Brussels, receiving its seal on 2 June 1960, unpublished. To be added at a later date as an appendix to the present work.
 F.H.Bradley, 1883, P.329."The Principles of Logic", London:Kegan Paul
 Bradley, p.260. Oxford, 2nd rev. ed, 1922t Vol. 1, p.285 (Chapter VI, first paragraph).
 "Textbook of Inductive Logic". L B. N. Roy, & Sons, 1956, Calcutta: S.C.Sarkar & Sons, pp.74-75
 N.A.Court,, New York: New American Library, 1958.
 B.T.Bell, New York: McGraw Hill, 1951.
 W.C.Vergara, New York: New American Library, 1957.
 D.Pedoe, London: Penguin Books, 1959. .
 I.Adler, New York- New American Library, 1957.
 W.W.Sawyer, London, Penguin Books, 1958.
 G. Verriest,"Les Nombres et les Espaces", Paris: Colin, 1956, pp.49-50, our translation.
 Eddington, Nat. Phys. World, p.226
 Verriest, p.94, our translation
 O.G. Sutton, "Mathematics in Action", London: G. 1958, pp.10 & 36, resp.
 Paris: Gautier-Villars, 1959.
 Published by the University of Paris, 1962,
 Bergson, "Metaphysique et Science", "OEuvres", p.1282, our translation
 "Le Grand Larousse Encyclopedique", Paris,1963 our translation.
 "Le Grand Larousse Encyclopedique", Paris,1963 our translation.
 Bergson, Intro. Meta., pp. 24-25.
 Bergson, D. et S.pp. 45-52,our trans.
 Bergson, D & S, pp.225-226, our translation
 Bergson, D & S, pp.226-227, our translation.
 Webster´s New Int.Dict.,2nd Ed..1934, p.528
 Trans. J.T. Coldthwait, Berkeley (Calif.) California Press, 1960
 Coll.Encyc, New York, 1958.
 See our article: "Memorandum on World Government",Values Vol.2: no.1 (Oct. 1956).
 See our two article series: "The Dialectics of Romance and Tragedy" (Parts I and 11), Values, Vol.3.- nos.10-11, (July, August 1958).
 Nataraja Guru, "The Bhagavad Gita, a Sublime Hymn of Dialectics Composed by the Antique Sage-Bard Vyasa", Bombay Publ., 1961.
 For clarification on this subject, see our articles: 1. "Towards a One World Economics," Values, Vol.7: nos.1-7 (Oct. 1961 - April 1962); and "Protolinguistics Applied to Economics," Values, Vol.7: no.3 (Dec. 1961
 Eddington, "The Philosophy of Physical Science", Univ. of Michigan Press, Ann Arbor ed., 1958, p.159.
 See our two article series on this interesting subject: "Man-Woman Dialectics". (Parts I & II), Values, Vol.5: nos.1-2 (Oct-Nov, 1959).
 The colophon translated into English reads as follows: "Thus ends in the Upanishads of the Songs of God, in the Science of the Wisdom of the Absolute, in the Dialogue between Sri Krishna and Arjuna."
 Bhagavad Gita, pp.2-20.
 These three figures are discussed by us in "The Word of the Guru", pp.187-206; and also in our article: "Vedanta Revalued and Restated" series (entitled "Varieties of Vedantism"), Values, Vol.9: no.11 (Aug. 1964).
 Madhavacharya, the author of the "Sarva-Darsana-Samgraha",who lived in the 14th Century, should not be confused with Madhva, the founder of the Dvaita (Dualistic) branch of Vedanta, who lived in the 13th Century.
 This idea of correlating or gathering together all the elements of wisdom into one unified whole is not something new. Socrates, in "The Republic", speaks about this in Book VII, 537. Johann Gottlieb Fichte also spoke about this in his writings.
 Verse I reads as follows:" I bow to Govinda, whose nature is Bliss Supreme who is the Sadguru (True Guru), visible through all Vedanta doctrines but otherwise invisible".
 "Word of the Guru", pp.106-122.
 Eddington, Phil.Phys. Sci., p10
 "Vedanta Sutras with Commentary of Sankaracharya", trans. G. Thibaut, ("Sacred Books of the East", Vols. 34 & 38) London: Oxford Univ. Press, 1890 & 1896; Delhi: Motilal Banarsidass ed., Vol l, p.61.
 A.N. Whitehead, "Science and the Modern World", New York: New American Library ed., 1961, p.83.
 Eddington, Phil.Phys. Sci., p11
 Eddington, Phil.Phys. Sci., p10
 Eddington, Phil.Phys. Sci., p.152