An Epistemology of Dharma as a Scientific Law -- Come Carpentier de Gourdon

Abstract: Dharma is a normative empirical concept derived from the observation of nature and the contemplation of the individual and collective self (inner nature) for the regulation of society in accordance with the laws of the universe. Further Dharma is the essential, non-material or “noumenal” character, sign or number (in the pythagorean-platonic sense: onoma-nomos, related to skt nama (rupa) of both the whole and each one of its parts. As such it is the identity of every phenomenon which is a process and not an object, perceptible only in its interaction with other processes, including our own sensorial perception rooted in our own ends (our dharma).

In that way, every dharma is a mathematical theorem and sanatana dharma can be described as an axiomatic meta-theorem, allowing us to describe the unified field of manifestation in its specifics and operating laws. Just as quantum physics describes atomic objects either as particles or as waves, dharmic epistemology regards all things as distinctive and yet as dynamic products of interactions between all other things - like the fractal quasi-crystals of physics and biology - in an indivisible web of being, the brahmajala.

Superficially Dharma and Science, at least in its “western” modern understanding, have very different meanings. Even in the Indian context, science in the traditional translation is vidya or jnana, while Dharma, from the root Dhru: to hold together, support or sustain (whose latin version is dur/us( - a), found in the roman maxim: Dura lex:  viz. the law is strict or hard, has both a biological and a moral significance, applying to the universe as a whole as to the human being in particular.

Further illustration of the semantic connotations of Dharma is provided by the latin words: firmus (firm), root of firmamentum (heaven or sky which holds all things) and frenus, hence ‘frein’ in French (brake) and ‘rein’ in English (1). In Avestan, the Iranian language akin to Samskrit the equivalent word is daena (whence the Arabic Deen) whereas Asha is the cosmic law (rta in Samskrit).

As Alain Danielou wrote: “For the Hindus, the world... is the realization of a divine plan in which all aspects are interconnected. Hindu society is the result of an attempt to situate man in the plan of creation” (2).

There is a relationship or organic link between Dharma and the Vedic cosmic law of rta (or ruta), a sanskrit cognate of the greek rythmos and the latin Ars and ratio in both arithmetical and moral senses: rate and reason, particularly if we think of the 17th century Classical European understanding of it as a divine regulatory principle as well as the highest human faculty and the Enlightenment notion of reason as the supreme law of society which the French Revolutionaries  promoted as a substitute for the Christian Biblical God. The eminent jurist Oliver Wendell Holmes referred to that notion when he spoke of “The path of law… (as) a trace of universal law…an echo of the infinite”.

As an additional illustration of Dharma’s semantic family, we can contemplate the relationship between the sanskrit dhru and the English verb “to draw”, from the common Old Indo European source. The very ambivalence of the term which denotes both the act of producing a graphic and the  extraction of water or any other substance or being (as in “drawing out) is manifested in the abstract use, as in “to draw a parallel” which can be interpreted either way.

Likewise Dharma is extracted from the observation of natural laws, as revealed to rishis in a state of samadhiin the form of Sruti but it is also drawn or mapped according to a transcendent archetype, as Plato’s nomos, related to the Sanskrit nama, the name which qualified and defines a thing, i.e; its law and role and also itsnumerus: number (both rational and irrational), the Pythagorean language of God related etymologically tonumen: what is perceptible only to the mind and not directly by the physical senses.

For Pythagoras as for Plato their number is the ultimate being of things as such; their ding an sich. Dharma is thus not promulgated but discovered in nature and in the mind that is a reflection of the former (as when the Buddha “set in motion” - in the minds of his disciples - the wheel of Dharma). As such it is axiomatic and may be called “the Divine Plan” and it is also comparable to the greek Ethos, the law and status of all beings and things decreed by Fate (Ananke) or by the gods.

Pythagoras will be mentioned on various occasions in the following. As the father of greek “scientific” cosmology and mathematics. The son of a Phoenician father and a Greek mother who studied in Egypt, Babylonia, Persia and probably India according to tradition, he practiced and taught many of the tenets of Brahminical wisdom, such as renouncing violence:ahimsa, vegetarianism, ascetism and fasting, reincarnation, meditation, prayer and communion with Nature which he described in a pantheistic manner as a living being filled with intelligent living forms.

He claimed to receive direct inspiration (sruti) from the gods and from the supreme soul of the universe and to keep the memory of everything (smriti) and he evinced supernatural powers similar to those of the yogis and rishis. He professed all creation to be regulated by the harmonics of sound (sabda, mantra) as the expression of numbers and he equated the dyad, the pair (dvandva in Samskrit) as a symbol of illusion as it is merely an effect of the duplication or self-reflection of the primordial One or source.

His teachings are fully consonant with the Vedic-Upanisadic metaphysics and appear to be at least in part derived from it. There is hence a clear connection between his definition of the cosmic law and the Indic notion of Dharma. He is reported to have said that the number 4 represents the principle of justice and in the Veda, the god Indra, the ruler of the skies, is worshipped as he who holds the four-armed vajra, emblem of his protective and destructive power. The centrality of the quaternary is shown in the fourfold division of theVedas, Varnas, Asramas, Purusarthas, Vamsas and other foundations of the Indian traditional social order.

Because it is the Law, or in other words the framework that makes reality, creation and life possible and durable, Dharma is inherently synonymous with the truth or essence of things (Sat-Satya), the first of the three terms which have been used to define the supreme being, with Cit: consciousness and Ananda: bliss. The Brihadaranyaka Upanishad (1.4,14) equates both (Dharma and Satya). Dharma is thus the essential characteristic or nature of things, both elementary and composite - a dimension of the word further developed in Buddhist philosophy - as heat and glow and the ability to burn are in the nature of fire or as expansion and gravitation are an essential property of the universe. As such, in grammar dharmin means bearer (of a property) as in the relation: sound is impermanent (i.e. is the bearer of impermanence).

In the human domain, Manava (human) Dharma however is not entirely innate as at least part of it must be learnt and consciously practiced in the form of duties, obligations and rites which characterise full cultured humaneness. Nature and culture complement each other as and when the latter is a faithful but refined reflection of the former in harmony with it. The Jaina religion divides Dharma into wordly (laukika) and unworldly (paralaukika) – for ascetics and renouncers who follow the yatidharma (pilgrim’s dharma) as opposed to the rules of conduct applying to the householders.

Rather early in the course of Indian civilisation, a correspondence was predicated between Dharma andAhimsa (harmlessness, later interpreted as non violence) which enshrines an evident principle of Indian spirituality as “live and let live”, - rather than the activist and often misapplied notion of “do goodism” highlighted in much of western religiosity - out of the reverent recognition of the innate freedom of all living beings and of respect for the diversity that characterises the created world. Indic wisdom therefore preaches non-interference, unless help is specifically sought in the right circumstances; otherwise, Karma following its course, an intervention, however well meaning, can be a form of violence and a misguided attempt to affect the natural order.

This acknowledgment of a predetermined course of events is no mere blind fatalism although it may be interpreted as such by many. Rather it stems from the awareness of Karma (action) as the manifestation of the Universal Dharma; the immanent activity of all things.

Nature itself (the Cosmos) is the effect of sanchita karma; the sum of all karmas which impact it in its present and previous states and phases. Each being and thing manifests and shapes its kriyamana karma by its behaviour which in turn is largely determined by past formative experiences and circumstances, theprarabdha karma. In this dynamic vision objects are inseparable from the acts that produce them and constitute their existence; being (bhu) and becoming (bhava), life (jiva) and action (kriya) are part and parcel of the whole, being is indeed “interbeing” as late Swami Ranganathananda used to say. The universe is adharma, as all are its component parts, whether fields, beings or particles. As another Greek “Oriental” sage Heraclitus said: “the One is born from all things and from the One all things are born” (Frag. 10).

Beyond the apparent ceaseless activity of nature, the steadfast, constant, stable character of Dharma is evoked by the term dharana, the first of the three highest steps according to Patanjali’s yoga sutras, which defines concentration in a seated position as the foundation of meditation and union with the Whole or Absolute.

For Buddhism, the doctrine in its abstract normative dimension is Abhidarma which, together with the Buddha’s discourse, sutra; and the rules of conduct, vinaya, cover all aspects of the teachings of Sakya Muni. In his fundamental teaching, the Buddha discloses and expounds on the Four Noble (or Cardinal), Truths, the fourth of which is Dharma: the way of Liberation or second ratna (jewel) and saranam (refuge) of the seekers, described as the Eightfold “Aryan” (arya astanga marga) Path, attained by observing and practicing truthfulness, clear sightedness  and righteous action in order to break out of the vicious circle of interdependent origination or pratitya samutpada that keeps all beings in thrall to suffering, illusion and death. Therefore, for many Buddhists, Dharma is inseparable from the Buddha and can be seen as another, formless aspect of his ultimate reality: tathagathagarbha.

As in Hindu doctrines, Dharma has three aspects, morality or ethics (sila), wisdom (prajna) and mental concentration (samadhi) in order to achieve unity with all things through control of the senses, emotions and mind which are all impermanent and ultimately unreal.

Further, especially in Buddhist metaphysics and epistemology of the Great Vehicle or “Broad Way” all objects and events in space and time (phenomena) are called dharmas because they manifest as and are contingent upon their respective inherent laws of being and becoming, so that they are indistinguishable from the essential principle that accounts for their appearance and persistence.

Beyond the apparently material realm, there are momentary mental states or conscious elements which may or may not be real, depending upon which school of Buddhist psychology one follows. Dharmas therefore arise out of the chain of dependent origination and are indeed called pratityasamutpadadharmas so that they are also artha (results)(3). There is hence a substantial nuance in the interpretation of the term although it may be noticed that various currents of Hindu philosophy have undergone similar evolution, probably under the influence of Buddhism.

The natural law is in the mind where it reveals itself: Justice, the motionless axial notion that regulates all things has its symbol in the Dharma chakra which was Vishnu’s emblem and which the Buddha sets in motion. It is the axle and also the spokes and the circumference: chakra = kuklos = the cycle. All its parts are also the wheel and are nothing when seen in isolation. All things derive their identity from their relation to the whole even if they are apparently separated from it. Otherwise they lose their leaning and become unidentified fragments; only their positions and roles give them a name and a meaningful identity:namarupa (name and form). According to the Pali canon, the Dharma is non-speculative, non-arbitrary, testable in practice, immediate in its application, universally valid and accessible only to the spiritual elite (the Aryas) and as such it is defined as scientific if we wish to use this modern notion.

Vishnu, the original Dharmaraja, has among its emblems, the shankha or conch whose shape is based on the logarithmic spiral, expressing the Golden Ratio (so named in the West by Fibonacci who brought to Europe the Indian numeral system from North Africa) and whose sound creates the universe, and as we said earlier, the chakra or wheel whose rotation symbolises the cosmic spheres and perpetuates the created world.

Various schools of Buddhist philosophy and cosmology define in great details a number of concepts and metaphysical domains related to the notion of Dharma. One of them is the Dharmakaya, the body of Dharma which is the supreme or essential being personified as Vairocana, beyond form, matter and senses (respectively Nirmanakaya and Sambhogakaya). Another is the Dharmadhatu: the domain or realm of Dharma, the highest heaven, the Empyreus of Hellenistic cosmologists, lying beyond both the form and the formless, beyond all created beings, including the gods, and where only dwell the Dhyani Buddhas, or transcendent principles.

Dharma as the Number or Code of Existence and Life: Hence Dharma is both a thing and its law, its number in the pythagorean sense, or logos (a cognate of the samskrt Loka) as alluded to by Heraclitus in his 50th Fragment:  “It is wise to heed not me but the Logos and to confess that all things are one”.

The word Muni which applies to the Buddha as well is related to the greek menein (stable in greek) andmonas: unity which in English has given rise to the word monk. Monas is the First Principle, as Pythagoras and Leibnitz defined it. The seed (bindu, dot in Samskrit) of a thing: ekatvam.

This introduction to the notion of Dharma and its virtual synonym Rta reveals that science insofar as it is a quest for truth and for the laws of Nature, has Dharma as both object and subject. Science draws laws from the observation of nature by exploring it in order to learn about it. It draws maps of nature while exploring it and inducts laws from observation; as we see in mathematics as in physics, astronomy and even in biology, representation is what enables us to make sense of what we study.

We don’t see the universe as it is but rather through pictures, charts and diagrams formed with the help of various instruments such as telescopes, radio-telescopes, microscopes, computer programmes, particle accelerators, bio-magnetic imagers, radio-scanners, X-ray machines and so on. As Heisenberg explained: “the smallest elements are not physical objects in the common sense, they are shapes, ideas which only the mathematical language allows to describe unambiguously”.

Indeed reflection leads us to conclude that not just the “smallest” (to us) elements but all things share this feature of essential inscrutability. Galileo stated four centuries ago: “Philosophy is written in this huge book which is always open in front of our eyes – I mean the universe – and we cannot understand it without having first to know the language and interpret the characters in which it is written. Indeed it is written in mathematical language”.

Like all equations, Phi, the Golden Ratio, is written in mathematical terms as a relation between numbers but it must be recalled that mathema in greek meant (mental) awakening and related to (omni)science, so that it is consonant, both in phonetically and semantically with the Sanskrit expression: Mahatma. The members of Pythagoras’s “Hemicycle” (his initiatic fraternity) were called mathematikoi, which means the all-knowing or awakened ones. Numbers are not only integers as we have noted in our reference to irrational numbers which, like the often paradoxical notions of relativity, non-Euclidian geometry, quantum theory and fractal quasi-crystal physics, always extend beyond the frontiers of our knowledge that they reshape in counter-intuitive ways.

The discovery of irrational numbers (which they called mute or ineffable) led post-pythagorean philosophers to separate geometry from arithmetic and the cognitive gap was only bridged by Descartes.

A good example of a counter-intuitive mathematical revelation is the fact that any number divided by zero is not, as the spontaneous guess would be, the number itself but the infinite. The Indians who conceptualized the zero in mathematical terms realized it, thus fully comprehending the character of that hitherto elusive notion. Infinite numbers like Pi etc… are other objects of meditation and computation is a synonym of belief so that mathematical thinking is much closer to “mystical” or metaphysical speculation than rational materialists think.

It is another matter that “western” science set as its goal since the Renaissance to acquire “physical” or mechanical mastery and control over the universe. This peculiar course has led modern scientists away from the traditional or Perennial Philosophy whose ultimate goal is to contemplate or celebrate the glory of creation by unravelling (without disenchanting or desacralising) the miraculous secret of its maker who is not separate from his/her creation (4). But when we examine the evolution of the natural and physical sciences and the insights they have gained in recent decades we will see that the nature (the bhutatathata or suchness of the Buddhists) of all things they investigate exhibit the properties enshrined in the polysemic and multifaceted concept of Dharma.

The latter may be equated, as we noted earlier, with the logos of Heraclitus, which expresses the unity of all things whose “conspiracy” (Vitruvius) between the parts and the whole is perceived as beauty both in natural and human creation. Adharma, the negation or Dharma is anrita; the cessation of rta, which is tantamount to death as a result of the breakdown in the “pre-established harmony”. Anrta has its remote echo in the latin english word inertia, which describes the features of non-living objects.

As the Scriptures say: Dharma when it is destroyed destroys and when it is protected (or upheld) it protects (or upholds):

Dharma anahato hante dharmoraksati raksita (Mahabharata, Vanaparva, 313. 128)

A brief study of the aforementioned Golden Ratio and its arithmetical expression, the Fibonacci’s series which was known to many ancient civilizations, including the Indian, Chinese, Mesopotamian, Egyptian and Pre-Columbian American ones, reveals that it expresses in mathematical and geometric terms the very notion of Rta and Dharma, in all the meanings we have described hitherto.

Wittgenstein, who seems to have known only western philosophy, warned in his Tractatus that in order to study science, one should forget about philosophy. However that caveat does not apply to Eastern thinking which sees all aspects of knowledge within a truly unified field of investigation and contemplation. A practical illustration of that convergence which reflects the very notion of Rta as “agreement” or “consonance” and further implying a circular or spiralic motion around a centre may be found in the underlying significance of the equation of the Golden Number (phi) – also the initial for the greek physis or Nature, written 

?= (1+   v5)/2

That relation expresses the proportion around which the universe as we know it is organized in its growth and stability laws, at all scales, from the infinitely minute to the infinitely large. The logarithmic or “golden” spiral that reflects this ratio manifests the reconciliation of harmonious though asymmetrical opposites by revolving around the point of origin: the bindu, aksara (primal sound) and stambha (pillar) of Creation. Like Dharma it is ever renewed and permanent in all its variations: eadem mutata resurgo.

The Golden Number illustrates the correspondence between Reason, both as a natural faculty and a rule of justice and ratio as a mathematical proportion. The same property defines Dharma which lays down the equation between all things, including ourselves and the universe that contains and includes them, called by Plato the “Just Mean” intrinsically related to Nagarjuna’s madhyamapratipad. Both Pythagoras and Plato related Law to the harmonic relations regulating the Cosmos and inherent to music.

In her remarkable work entitled “Divine Proportion: Phi in Art, Nature and Science”, Priya Hemenway defines the Golden Section (thus called by Fibonacci and formalized by Martin Ohm) as a “formula that serves as a key to a Great Unifying Principle” and she notes: “when we ponder our place in this equation, we discover that we are at once the whole, the largest part of the whole and also the smallest, in an unvaryingly balanced ratio of the whole to the largest part and of the later to the smallest”.

She further explains: “There is a mathematically demonstrable relation, generating patterns and dynamics diffused all over in nature. The laws of proportion used by artists are derived from it and also in the spiritual field, those principles of harmony are seen as a fundamental truth… They even determine the proportion of our physical bodies” and were defined by Jay Hambidge as a dynamic fundamental symmetry of Nature which lies at the core of traditional art forms worldwide.

The American philosopher, scientist and artist Walter Russell illustrated that cosmic law of harmony in his monumental life work (5). Harmonia in mythology is said to be the daughter of Ares (Arya: aryadharma - as Dharma is presented as father to Hari (Visnu) - or of Hephaistos (Tvstir), the architect and builder of the Cosmos: Visvakarma.

It is important to point out that Phi is an irrational number, illustrating the fact that natural law is not reducible to the ratio of an integer and as such has no definite digital representation. It can only be represented by the operation that determines it, because it is a process and not an object. That suggests something very profound by analogy about the character of natural laws. The innumerable dharmas of all beings and things, as well as their common essence or principle the Sanatana or Samanya Dharma may be described as fractal patterns (Mandelbrot sets) in which all parts are similar to the whole (self-similarity principle) though they retain their individuality and symmetry.

Mathematics enunciates its laws through theorems which can be seen as translations of the concept ofdharma. A word like ‘triangle’ for instance describes a  geometrical object shaped according to the mathematical laws applying to a flat surface containing three angles; however the specific shape of a triangle reflects its particular properties (i.e. isosceles, equilateral, rectangle). Likewise there is a more general dharma for a species and a more specific one (visesa) for each sub-species, family and individual. Further for the human being who wishes to attain enlightenment and liberation from the trammels of cyclical mortal existence, there is a transcendental (ekantika) dharma.

Indeed, theorems (a word derived from the greek verb “consider, examine, observe”, related to theoros: spectator and theater) are defined as statements proven on the basis of previously established statements (other theorems) or accepted but not necessarily proven statements (axioms). Theorems, at least in mathematical language are necessary consequences of hypotheses and are hence deductive though they almost always involve elements of empirical evidence and speculation. In physics too, theorems or laws inevitably involve assumptions and intuitions.

Theorems can also generally be described as laws or principles and cannot always be formally proven to be true. They are used as building bricks for formal theories or systems which in turn can be defined or characterized by “wider” theorems known as “metatheorems”. Therefore, Dharma, especially in its timelesssanatana form (Pali akaliko dhammo for Theravada Buddhists) is a metatheorem about the universe defined as a formal system such as, for instance, the “Net of Indra” or “Golden Egg of Brahma” (hiranyagarbha).

The cosmos is defined in contemporary physics as a “network of interactive events”, rather like themayasamsara of Hindu and Buddhist metaphysics and we can try to show how the patterns and processes mapped out by contemporary research are quite consistent with the concepts laid out in the cosmologicalsastras of Indic literatures which have influenced the spiritual and scientific heritage of most of East Asia.

Until recently it was thought that chaos and order were two separate realities, the former denoting the amorphous and inanimate world while the latter was characteristic of living organizations. However in recent decades, the discovery of the properties of fractals by Mandelbrot, Penrose and others has led to a gradual unification of chaos and order which was already central to many ancient philosophical systems of Asia such Hinduism, Buddhism and Taoism.

For instance, the basic notions derived from the study of crystallography were anticipated by the Indic descriptions of Indra’s jeweled net (indrajala or brahmajala for Buddhists), the Tantric Vajrayantra (tantrameans network, web) in which “diamonds” are packed and ordered periodically and symmetrically like knots or links in a fabric or like the atoms and molecules of a crystal. Alan Watts describes it as “a multidimensional spider’s web in the early morning, covered with dew drops. And every dew drop contains the reflection of all the other dew drops… And so on ad infinitum…” (6).

Analogies with contemporary research in this area of geometry and physics are provided in the book Indra’s Pearl, The Vision of Felix Klein (2002) by Mumford, Series and Wright and the image of Indra’s net was used by Douglad Hofstader in his well-known work Godel, Escher and Bach to explain the structure of complex interconnected networks.

As Priya Hemenway explains in her book, the discovery of quasi-crystals, which appear to be the fundamental structures for life (such as biotic cells) and are packed in an orderly, aperiodical but non-amorphous sequence, reveals a hitherto unknown state of matter and, even more significantly, enables us to peer into a wondrous cosmic process: the interaction between neighbouring atomic clusters can lead to the formation of stable and dynamic solid born out of sharing between them.

The creation of such new structures that do not diminish or disrupt their co-creators takes place through a series of “discrete atomic jumps” or phasons, illustrating the property described in Isopanisad as purnasya purnamadaya purnat purnam udacyate and provides a tangible parallel to the Vedic concept of yajna or sacrifice of the One to give birth to the many and of the many to reintegrate Oneness, in a cyclical process of expansion  or translation of the One into the plural (Brahman, from brih) and of return of  the many dharmas into the Dharma at the source that pervades (Visnu, from Vis) all.

Mathematics, physics and biology can therefore be understood as tools to observe and describe the ceaseless rotation of the wheel of Dharma at all levels of manifestation.

1)      Article dharma in wikipedia, last checked on 12 August 2012, 3 p.m.

2)    “Virtue, Success, Pleasure and Liberation –The Four Aims of Life in the Tradition of Ancient India” (1993) by Alain Danielou, quoted in Sadhu Vivekjivandas “Hinduism – An Introduction” Part II,  (Swaminarayan Aksarpith, Ahmedabad 2010).

3)     “Nagarjuna, The Philosophy of the Middle Way”, David Kalupahana, SUNY Press (1986).

4)     Jon Lilly: “The miracle is that the universe has created a part of itself meant to study the other part and that this part, by studying itself, ends up finding the rest of the universe in its natural and internal reality” (quoted in  “Divine Proportion” by Priya Hemenway, Stirling Publishing House, 2008).

5)     “The Secret of Light” (1947) and “The Message of the Divine Iliad” (1948-49) by Walter Russell.

6)    “Following the Middle Way”, Alan Watts, podcast.com 2008.08.31, quoted on Wikipedia article Net of Indra, checked on 12 August 2012, 3,30 pm.

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