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from One Form to Another


The Interaction of Colour and the Elements

Some Scientific and Aesthetic Considerations.

A. Ranganathan


Since time immemorial, man has been fascinated by the blue sky,1 the blue of the sea, the beauties of the sunrise and sunset, the halo around the moon, the reflections in placid lakes, the loveliness of the rainbows and the exquisitely beautiful colour schemes in great works of art. Naturally great poets have immortalized the skies and seas. For example, one is reminded of the beautiful lines of Shelley in his Adonais:

As long as skies are blue, and fields are green

Evening must usher night, night urge the morrow.

To cite another example, Byron wrote in his Childe Harold’s Pilgrimage:

Roll on, thou deep and dark blue ocean, roll!

Again, the neon lights and the laser technologies which flash through the modern cities, constitute a new addition to a series of visual impressions and manifestations. Moreover, it is worthnoting that the interaction of light with matter results in several phenomena — reflection, refraction, scattering or absorption of light by the objects, which reveal the presence of the objects as well as their colours.

It is interesting to reflect on the fact that the eye which perceives these colours is sensitive to a small range of the electromagnetic spectrum which is the 400 to 700 nanometer (billionth of a meter) wavelength region or the violet to red radiation of the visible spectrum. Also the interaction of colour with the elements is based on the physical theory that the electrons in atoms and molecules occupy various discrete energy levels. Again the incident light directs energy to these electrons and raises them in an excited state to higher, unstable energy states. Naturally these electrons fall from an excited state to the lower lying ones by emitting photons. And the perception of colour arises when these photons carry energies ranging between 1.77 and 3.1 electron volts, corresponding to the wavelengths of the red and violet colour light.

The interaction of colour and the five elements — earth, water, fire, air and the sky (akasa) — illuminates not only several disciplines such as Indian philosophy, Western philosophy, comparative aesthetics, modern physics and photochemistry, but also highlights the physics of elementary particles which had inspired Werner Heisenberg’s essay on ‘The Representation of Nature in Contemporary Physics’.2 Again, in actuality, colour (except at the microscopic level of particle physics) is a strikingly visible manifestation of some of the subtle effects that constitute the structure of matter. Not surprisingly, the interaction of light waves with electrons is a major preoccupation of twentieth century physics. For the duality between wave and particle aspects concerning light is now adopted to describe the properties of matter. And Prof. N. Bloembergen argued in his lecture ‘Reflections on Light’3 that "in the beginning of the twentieth century, the concept of light particles was revived by the theoretical studies of Planck and Einstein regarding the nature of Black-body radiations".

This paper is confined to a discussion of such concepts as Ananda Coomaraswamy’s explanation of the Indian theory of painting, the scientific basis of Leonardo da Vinci’s Treatise on Painting, the mathematical inadequacy of Goethe’s Theory of Colour in contrast with the abstract reasoning of Newton’s Opticks, the Rayleigh explanation of the blue sky, C.V. Raman’s explanation of the blue colour of the Mediterranean Sea, Professor Penrose’s Holistic theory of Physics, Psychology and Neurophysiology, Professor Chandrasekhar’s bifocal view4 of the patterns of creativity that constitute the landscapes of General Relativity and the Series Paintings of Claude Monet and the rediscovery of the Pythagorean idea of a "pre-established harmony" in Gell-Mann’s world of quantum numbers. Furthermore, an attempt will be made to underscore the relevance of Leonardo da Vinci’s holistic view of colour — which embraced the earliest scientific explanation of the blue sky as well as the theory underlying the colour schemes in Renaissance paintings — to the modern world of Rayleigh Scattering (derived from the theory that the scattering of sunlight by particles in the atmosphere is proportional to the inverse fourth power of the wavelength and thereby contributes to the blue colour of the sky) and the contemporary marvels of colour photography and the television industry based on colour technology.

Viewed historically, it is a tribute to the versatility of the Leonardesque mind, that some of Leonardo’s reflections on the nature of Renaissance Paintings contribute to a deeper understanding of Ananda Coomaraswamy’s Indian view of Aesthetics. Indeed, in his major works of scholarship entitled History of Indian and Indonesian Art, The Transformation of Nature in Art, Christian and Oriental Philosophy of Art, What is Civilization and other Essays and Essays in Early Indian Architecture and in his technical essays such as The Technique and Theory of Indian Painting Coomaraswamy dealt with the meaning of Indian art, the philosophical symbolism which is its distinguishing characteristic and the Indian aesthetic view derived from the thesis that "the eyes are extended to meet the ears no less in colour than in word-painting". Here, it is worthnoting that the representation of the human form is not an end in itself, even in the European artistic context. As Leonardo da Vinci emphasized in his Treatise on Painting: "That figure is most laudable which by itself action expresses the passion which animates it". For he noted that a sophisticated painter ought to know anatomy.

The memorable quality of the mural of the Last Supper in Santa Maria Delle Grazie relies no less upon Leonardo’s religious passion than upon his use of the anatomical form, subtle chiaroscuro and aerial perspective. However, the canons and conventions of Indian art are different. Indeed Coomaraswamy argued5 in his essay on The Technique and Theory of Indian Painting that: "The Indian artist sees indeed ideally, but he does not idealize, he imitates. He does not draw according to his taste but from the intellectual image; not ‘knowing what he likes’ but liking what he knows . . . The Indian artist painted in the express likeness of what he saw ‘as if in a mirror’, and yet not such a ‘looking-glass image’ as we see in the mirror . . . That art is essentially an intellectual act is a conception remote indeed from the contemporary view of art as a sensational experience which view is also presupposed in the unsatisfactory word ‘aesthetic’, for which there is no Sanskrit equivalent; but it cannot be distinguished from the view of art that prevailed in Europe throughout the middle ages and of which full account must be taken by every serious student of Byzantine or Romanesque".

In one of his great scientific essays, Leonardo da Vinci referred to his discovery (made at a time when modern physics was not even in its infancy) that the sky became much darker while scaling the Alpine Peak of Mount Rosa. For da Vinci had intuitively realized that the blue sky was simply the blue light of the sun which is visually rerouted to us through dust and air molecules. Interestingly, commenting on Rayleigh’s explanation of the blue colour of the sky which was formulated several centuries later, Prof. C.V. Raman remarked6 in his work on The Physiology of Vision that it was "a consequence of the masking or suppression of all the other colours in the spectrum by its blue section". However, it is seldom realized that Leonardo da Vinci’s explanation had anticipated the mathematically sophisticated theory of Lord Rayleigh relating to the colour of the sky by several centuries.

Just as Plato is said to have inscribed "Let no man ignorant of geometry enter here" above the entrance to his Academy, so did Leonardo da Vinci proclaim "Let no one read me who is not a mathematician". Indeed, according to Leonardo, his work Treatise on Painting was an extension of the theory that "Painting is a Science". For Leonardo’s great paintings were based on geometric principles. Actually, his Treatise on Painting is a fascinating example of the dialogue of scientific and aesthetic cultures. Not surprisingly, Leonardo da Vinci had discussed the effect of air as well as of light on what he termed the "obscuring medium" intervening between the eye and the object. And this line of enquiry enabled him to study the impact of distance on objects and the manner in which their colour is partially changed by the environment.

Leonardo da Vinci wrote in one of his Notebooks,7 "There is no certainty where one can neither apply any of the mathematical sciences nor any of those which are based on the mathematical sciences". What Leonardo wished to emphasize was the inadequacy of an observation of a natural phenomenon in qualitative terms. This thesis naturally reinforced the relevance of accurate measurements and quantitative relations to a study of natural phenomena. Travelling back in time, one notes the historic role of Pythagoras — in realizing that qualitative differences in sense perception are based on mathematical reasoning. Significantly Professor S. Chandrasekhar adverts to just the relationship derived from scientific exactitude and aesthetic meaning in his Lecture, "Shakespeare, Newton and Beethoven or Patterns of Creativity": "The discovery by Pythagoras that vibrating strings, under equal tension sound together harmoniously, if their lengths are in simple numerical ratios, established for the first time a profound connection between the intelligible and the beautiful. I think we may agree with Heisenberg that this ‘is one of the truly momentous discoveries of mankind’." Here one can make a similar jump in time to the ancient Indian era, to realize how an equally ancient stream of aesthetics — for instance, that based on the acoustical perfection of the ancient Indian drum — bears what Professor Raman noted as the "remarkable testimony to the inventiveness and musical taste of its progenitors".

Leonardo da Vinci had stated in his Treatise on Painting that "there are three parts of Perspective as used in Painting: of them, the first includes the diminution in the size of opaque objects, the second treats of the diminution and loss of outline of opaque objects, and the third treats of the diminution and loss of colour at large distance." He characterized them Linear Perspective, Perspective of Disappearance and Perspective of Colour respectively. Commenting on the Perspective of Disappearance, Leonardo wrote: "Every object as it becomes more remote loses first those parts which are slenderest. Thus of a horse, one would lose the legs before the head, because the legs are thinner than the head; and the neck before the body for the same reason. Hence it follows that the last part of the horse which could be discernible by the eye would be the mass of the body in an oval, or rather in a cylindrical form, and of this one would lose its thickness before its length." Naturally he advises the painter: "You must diminish the definiteness of outline of objects in proportion to their increasing distance from the eye of the spectator." This argument led on to the conclusion that objects become bluer as a result of the distance due to the colour of the intervening air. And this change of colour towards the blue becomes more pronounced in the shadow or with the darker colours than with the lighter ones. As he put it, "you know that in an atmosphere of equal density the remotest objects seen through it, as mountains, in consequences of the great quantity of atmosphere between your eye and then appear blue . . . . . Hence you must make the nearest building of its true colour, but make the more distant ones less defined and bluer. Those who wish to look farther away you must make them proportionately bluer."

Here is Leonardo’s advice to the painter: "Take care that the Perspective of Colour does not disagree with the size of objects, that is, that the colours diminish as much from their natural strength in proportion as the objects at various distances diminish from their natural size". Elsewhere Leonardo wrote in the same strain: "White, is no colour of itself, it changes and adopts part of the colours around it . . . That side of a woman which is illuminated by the light from the sky will have a bluish hue. Should she stand near a meadow between the sunlit grass and the sun itself, the folds of the gown of which the light of the meadow will show the reflected light on the green meadow." In other words, Leonardo had visualized some of the ideas of the Impressionists.

Leonardo da Vinci was familiar with the techniques of the masters of early Renaissance Painting, who knew the effect of light and shade in highlighting the form of objects. In fact, Masaccio had experimented with light and shade in modelling his forms. However, Leonardo was the first painter to introduce the concept of space around his figures in order to work out the compositional unity of his paintings resulting movement which had inspired the artistic imagination of Rembrandt. And significantly enough, Leonardo observed "that a Painter is not Admirable unless He is Universal."

Seen in the historical perspective, the eminent scientist-artist Leonardo da Vinci who preceded Goethe by several centuries had visualized the Rayleigh theory of the blue sky. It is interesting to note that the word Chiaroscuro is derived from the Italian terms Chiaro (‘Light’ or ‘Bright’) and Oscuro (‘Dark’ or ‘Shade’) and reveals the modelling of forms through the use of light and shadow. Furthermore it is well to remember that though the technique of Chiaroscuro had been discovered by the Greek painters in the Hellenistic age and was also used by the Roman painters, it was forgotten during the dark middle ages. Indeed there is an historical appropriateness in the fact that the technique of Chiaroscuro was rediscovered during the Renaissance. And just as Leonardo had anticipated the wave-nature of Sound in his Notebooks, his studied emphasis on the technique of Chiaroscuro inspired Rembrandt’s Night Watch. Incidentally, it is not generally realized that Rembrandt had actually intended to highlight a scene in the late afternoon. In fact, when the painting was cleaned in the mid-forties, it became clear that its nocturnal effect was due to the darkening of the layers of varnish that had been applied over the paint. It is certainly a tribute to Rembrandt’s expertise in the application of the technique of Chiaroscuro that the painting had darkened to such an extent that it is difficult to determine whether the scene had taken place during the day or night! For this great painting, which can be described as a Chiaroscuro in a Chiaroscuro, is a tribute to Leonardo da Vinci and Caravaggio. Small wonder that the great mathematician-philosopher Prof. A.N. Whitehead argued in his Science and the Modern World8 that Leonardo da Vinci’s emphasis on "the patient observational habits of the naturalistic artists" as well as the Leonardo contribution to "the practice of physics" had contributed to the scientific imagination of the modern world.

Leonardo’s Treatise on Painting is relevant to the contemporary artistic scene even today. For Leonardo flourished in an era which was not familiar with the well-known scientific fact that red, green and blue are the primary colours which can additively produce any shade between red and violet in the visible spectrum. Furthermore this idea is imaginatively used in modern colour technology. Yet it is truly remarkable that Leonardo had an intuitive understanding of this scientific fact. Actually Leonardo da Vinci argued that "Green and blue are invariably accentuated in the half-shadows, yellow and red and white in the highlights." And the argument relating to the primary colours in Leonardo’s Treatise on Painting to the modern theory — derived from ‘The Three Colour Principle’ — which forms the basis of the commercial exploitation of the physics of colours in the areas of colour photography as well as colour television of the modern colour television industry.

Johann Wolfgang von Goethe, the great German poet and author of the classic Faust is also known for his scientific studies ranging across The Theory of Colour Comparative Anatomy and Plant Morphology. Actually he is renowned for his pioneering contribution as the earliest historian of science. However, his work on The Theory of Colour is not only controversial but also unconvincing on three counts. First, Goethe proceeded on the assumption that the mathematical principles underlying Newton’s experiment with the prism had clashed with his belief that the human organism is the best instrument for studying nature. Naturally Goethe tried to argue that Newton was wrong in demonstrating that coloured lights could be combined to form white light. Again, arguing in this strain, Goethe rejected Newton’s scientifically acceptable theory that light rays themselves are not coloured but that the sensation of colour is registered in the brain. For Goethe rejected not only the well-known Newtonian principle that coloured lights could be combined to form white light but also suggested (without adducing any evidence) that all coloured lights were mixtures of light and darkness.

Second, Goethe maintained that The Theory of Colour as he viewed it,9 "has been hurt and greatly hindered in its progress by being lumped with the area of optics dependent on geometry. It may, in fact, be considered entirely separate from geometry". In fact, Goethe also argued10 that "another problem arose because a fine mathematician [the reference is to Newton] had adopted a completely false concept of the physical origin of colour; his great accomplishments as a geometrician long served to sanction his scientific error in a world ruled by constant prejudice." For, according to Goethe, "light is one and indivisible"— a phenomenon which cannot be interpreted by any theory of particles! And Goethe observed: "No group with aristocratic pretentions has ever looked down on outsiders with such insufferable arrogance as the Newtonian school has shown from the beginning in dismissing everything accomplished before its founding and beyond its confines". Surely this Goethe observation is not convincing. And, as Bertrand Russell wrote wittily in An Outline of Philosophy: "Physics is mathematical not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover!"

Finally, Goethe commented that Newton’s Opticks could be "compared to an old castle originally laid out by the builder with youthful impetuosity and later expanded and furnished as required by time and circumstance. It was then gradually fortified and secured against strife and enemy attack." Indeed, Sir Isaac Newton cannot be disposed of that easily. Here are two Queries from Newton’s work on Opticks which had been published in 1704: "Do not Bodies act upon Light at a distance, and by their action bend its Rays?" and "Are not gross Bodies and Light convertible into one another?" These Queries clearly reveal that Newton was conjecturing the gravitational bending of light and the equivalence of mass and energy — which are the main consequences of the General and Special Theories of Relativity — and which were formulated by Einstein two centuries or so after the death of Newton. And in the ultimate analysis, Goethe’s Theory of Colour — based on his reflections on colours and colour perception, more subjective than scientifically convincing — can at best be viewed as a spectrum of individualistic responses to Newton’s Theory of Light in the history of ideas.

In the "History of Science", observed Professor C.V. Raman in his 1930 Nobel Lecture,11 "we often find that the study of some natural phenomenon has been the starting point in the development of a new branch of knowledge". Indeed Lord Rayleigh’s observations concerning the colour of the sky and their experimental verification by Cabannes, as well as Raman’s experiments and theoretical formulations on the colour of the sea are not only two major essays in the borderland between Optics and Aesthetics, but also reinforce the Raman thesis that the study of natural phenomena constitute the starting points in the development of new branches of knowledge.

Lord Rayleigh had calculated the number of molecules in a unit of volume in air, while enjoying the scenery of Mount Everest from the terrace of his hotel, in 1899. Again, while viewing the dimness of this towering Himalayan mountain’s outline, Rayleigh concluded that an appreciable part of its light was scattered away. He found that the scattered light was conspicuously blue as a result of the radiation which varied with the fourth power of the frequency. For he noted that the higher frequencies were re-emitted even more powerfully than the lower ones. This piece of mathematical reasoning enabled Rayleigh to determine the scattering power of each molecule from the refractive index of air. Furthermore, it led to the result that the number of air molecules per cubic centimeter at sea level were 3 X 1019 — a result which was experimentally confirmed by Cabannes. In fact the work of Rayleigh and Cabannes had provided not only the theoretical and experimental framework for the blue colour of the sky but also established the fact the air molecules were non-spherical in the wake of a depolarization effect. At the other end of the spectrum, it is well to remember that Raman had climbed the Dodabetta in the Nilgiris to measure the depolarization of the light scattered by the sky. And Raman attributed12 the residual depolarization to the anisotropic (possessing different physical properties in different directions) nature of the air molecules.

The validity of the subsequent Rayleigh theory that "the much-admired dark blue of the deep sea is simply the blue of the sky seen by reflection"13 was questioned by Raman while voyaging through the Mediterranean and Red Seas in 1921. In fact, even on board the ship Raman felt that the Einstein-Smoluchowski concept of thermodynamic fluctuations — which was developed to explain special optical phenomena near the critical point — could be extended to explain molecular diffraction in liquids. It was this characteristic intuitive flash that explains the memorability of the Raman paper on the colour of the Mediterranean Sea. Actually, in the wake of quenching the surface reflection of the sky in the sea through a polarising Nicol Prism at the Brewesterian angle, Raman observed that the colour of the sea was not only impoverished but actually spectacularly improved. It was clear therefore that the blue Opalescence of the Mediterranean Sea was due to the scattering of the sunlight by the molecules of the water.

The visual impact of the blue of the Mediterranean Sea on Professor Raman’s scientific imagination led on to the 1922 Royal Society Paper ‘On the Molecular Scattering of Light in Water and the Colour of the Sea’.14 Actually, the theory underlying this discovery is based on the fact that the variations of density owing to molecular vibrations or fluctuations alter the refractive index of the fluid and thus result in the scattering of Light. Raman demonstrated that water at thirty degrees centigrade ought to scatter light 160 times as intensely as dust-free air under normal conditions. He arrived at the result that 50-metre deep water appeared as blue as the Zenith Sky if the absorption of water is not considered. At this point Raman applied a correction for absorption by working out a satisfying agreement between theory and observation. And in his concluding remarks, he wrote that "a sufficiently deep layer of pure water exhibits by molecular scattering a deep blue colour more saturated than skylight and of comparable intensity. The colour is primarily due to diffraction, the absorption only making it of a fuller hue."

This celebrated paper on the colour of the Mediterranean Sea resulted in the discovery named after him — which is known as the Raman Effect. Indeed, commenting on the Raman Effect which was discovered in 1928, Albert Einstein observed that "C.V. Raman was the first to recognize and demonstrate that the energy of the photon can undergo a partial transformation within matter." Again, the paper on the Mediterranean Sea is also as much a fundamental contribution to Optics as it is to Visual Aesthetics. For the Raman paper recalls an aesthetic sensibility that one can still experience while reading Galileo Galilei’s Starry Messenger which recorded the first Galilean sight of the night sky through a telescope. And viewed in retrospect, it is interesting to note that Raman had transformed the sky at Dodabetta in the Nilgiris and the Sea (while voyaging through the Mediterranean Sea) into laboratories!

It is well-known that Professor Raman devoted an important phase of his career to an understanding of colour phenomena. In fact, he was concerned with the fundamental importance of colour in several scientific disciplines. Here it is interesting to recall Raman’s ‘sight-seeing’ at Mount Wilson Observatory in 1924. And commenting on the account relating to Professor Raman’s ‘sight-seeing’ at Mount Wilson Observatory, Professor S. Ramaseshan observed:15 "During a visit to California (in 1924) Raman viewed the nebulae through the 60-inch and 100-inch telescopes of Mount Wilson Observatory near Pasadena. He recounted vividly that the Right nebula Lyra exhibited flaming colours changing progressively from the external edge of its ring to its inner margin while the great nebula in Orion was a blazing area of variegated colour determined by the line emission of gases of which it is composed." Obviously Raman’s ‘sight-seeing’ was rewarding during the two nights at Mount Wilson Observatory. For he was able to view the Orion and Ring Nebulae closely despite the fact that the two nebulae are more than 180 degrees apart on the sky. And in his essay on "A Celebration of Colour in Astronomy" Dr. David Malin of the Anglo-Australian Observatory in Sydney, Australia remarks16 that the Raman ‘sight-seeing’17 at Mount Wilson Observatory "is the only account I know of where the colours of astronomical objects are so vividly described."

Just as Professor Niels Bohr formulated his principle of complementarity in the wider perspectives of physics and philosophy, Professor C.V. Raman related the perception of colour in some areas of physics and astronomy to a holistic perception which included the application of the Quantum Theory of Light to Physiology and human consciousness in its sweep. For Raman’s intellectual heroes were Leonardo da Vinci and Herman von Helmholtz. Indeed, the similarities are truly striking. In fact, Niels Bohr worked out a philosophical framework for the theory of Complementarity in order to discover the "great inter-relationships between all areas of knowledge." Actually Bohr had propounded the philosophy of The Unity of Human Knowledge,18 with special reference to the basic areas of Classical Physics, Quantum Physics, Physiology, Philosophy and Schroedinger’s work on the substance of life (1960). In fact, his aim was to "promote mutual understanding between nations with very different cultural backgrounds." Actually, Bohr had already presented to different audiences his holistic perceptions, such as "Causality and Complementarity" at the Second International Congress for the Unity of Science, Copenhagen, 1936, "Biology and Atomic Physics" at the International Congress for Physics and Biology, Copenhagen, 1937, and "Natural Philosophy and Human Culture" at the International Congress for Anthropology and Ethnology, Copenhagen, 1938. And interestingly enough, Professor C.V. Raman had cut across the differences between the classical description and the quantum description of physical phenomena in a philosophical sense in an essay, "The Molecular Diffraction of Light",19 which was published as early as 1922.

Raman’s holistic perception of colour has an epic grandeur which is similar to Bohr’s philosophy of Complementarity. In the words of Professor Raman, the inter-disciplinary questions derived from the perception of colour "touch the two great fields of exact knowledge and a third field of which at present we have only glimpses. The first field is physics and what it has to tell us about the nature of light, its properties and behaviour. The second is physiology, which concerns itself with the structure and functioning of the sense-organs, such as our eyes, and their connections with the cerebral centres. The third field of knowledge lies where mind and matter meet and we seek to penetrate the mystery of human consciousness and its awareness of the external world. And it is by bringing the physical and physiological aspects of our problem simultaneously into focus that one can hope to find satisfactory answers on the material plane to the questions which interest us."

It is well to remember that Raman had arrived at his holistic perception of colour during the pre-computer era of modern science. In a sense, Raman’s argument was continued by Roger Penrose in his recent publication The Emperor’s New Mind: Concerning Computers, Minds and the Laws of Physics.20 In fact, Professor Penrose’s work is a piece of writing woven together through an entertaining and extensive commentary which affords a visionary glimpse of the possible connections between the mathematical universe of twentieth century physics and the world of consciousness. Indeed, Professor Penrose links his vision of a new theory of physics with the phenomenon of consciousness in the new areas of psychology and neurophysiology. Actually, his assertion that Quantum Gravity must be time-asymmetric is startling. For it may be difficult for the physicists, who believe that Quantum Physics and Relativity are time-symmetrical in a setting where their equations work equally well whether they run forward or in reverse, to accept the Penrose viewpoint that time will flow from the past toward the future and not in reverse. And the distinction of this work lies in Professor Penrose’s ability — despite some disagreements on certain issues — to arrive at a new holistic perception derived from a variety of disciplines such as Cosmology, Relativistic Dynamics, Neurophysiology and Mathematical Logic.

At this point, it is necessary to refer to Query 28 of his historic publication Opticks in which Sir Isaac Newton rejected the wave theory of light. Here the controversy centering round the Wave and Corpuscular Theories of Light is not important. What is important, however, is Newton’s inspired use of the metaphor in physics. Indeed, in his 1672 paper on light and colour, which was published in the Philosophical Transactions of the Royal Society, Newton described his famous experiment with a prism. In fact, Newton darkened his chamber and allowed a ray of sunlight to enter a prism, enabling it to spread out into the the colours on the opposite wall. Actually, this experiment with a prism formed the basis of Newton’s explanation of this phenomenon in terms of a theory of Light. Similarly Maxwell’s mechanical model for a mathematical conceptualization of electricity and magnetism, including the ether, was obviously a piece of fiction. However, it helped Maxwell to work out the correct equations. And Professor Chandrasekhar’s visualization of the phenomenon of Alice crossing the ‘event horizon’ in Lewis Carroll’s Through the Looking Glass — as illustrated in the well-known Chandrasekhar paper "How One May Explore the Physical Content of the General Theory of Relativity" — is yet another inspired use of the metaphor in physics. Professor Chandrasekhar argues21 that the solutions (worked out by S. Chandrasekhar and Basilis Xanthopoulos) for both the Einstein vacuum and the Einstein-Maxwell equations had upset the then held conventional belief that the collision of waves would lead on to the development of curvature singularities. Indeed, in Professor Chandrasekhar’s words,22 "One found instead that event horizons formed; and a further domain which included hyperbolic arc-like singularities reminiscent of the Kerr and the Kerr-Newman black holes." Actually this situation is conceptualized in a delightfully different context by Lewis Carroll (the pen-name of the nineteenth-century Oxford mathematician Charles Lutwidge Dodgson) in his celebrated work Through the Looking Glass which is meant for children. In fact, Professor Chandrasekhar creates an ambience, at once mathematical and literary, which suggests Alice’s intimations of Space-Time Through the Looking Glass: "It (the passage through the Looking Glass House) is like our passage as far as you can see, only you know it may be quite different on beyond".

Among the most remarkable features of Einstein’s General Theory of Relativity is its vitality. For the consequences of the General Theory can be glimpsed in a number of disciplines ranging from literary criticism and aesthetics to the astrophysics of black holes, colliding gravitational waves and the non-radial oscillation of stars. For example, Professor Whitehead states in his Science and the Modern World that the great Greek tragedians Aeschylus, Sophocles and Euripides are the pilgrim fathers of the modern scientific imagination. Indeed, in a celebrated argument, Professor Whitehead recreates the dramatic significance in the very staging of that historic meeting of the Royal Society which enabled him to witness the Eddington verification of the General Theory of Relativity in a Newtonian ambience. For, he explains that the essence of dramatic tragedy is not unhappiness, but that remorseless inevitableness that pervades scientific thought.

Commenting on Professor Heisenberg’s aesthetic criterion that "Beauty is the proper conformity of the parts to one another and to the whole", Professor Chandrasekhar says23 that it is complementary to the aesthetic criterion of Francis Bacon: "There is excellent beauty that hath not some strangeness in its proportion." Chandrasekhar argues that the General Theory of Relativity has some strangeness in the Bacon-Heisenberg sense. For "It consists primarily, in relating, in juxtaposition, two fundamental concepts which had, till then been considered as entirely independent; the concepts of space and time on the one hand, and the concepts of matter and motion on the other." Thus, "in the fusion of gravity and metric that followed, Einstein accomplished in 1915 what Reinmann had prophesied in 1854, namely, the metric field must be causally connected with matter and its motion." And Chandrasekhar concludes that the "greatest strangeness in the proportion consists in our altered view of space-time."

In his discourse24 "The Role of General Relativity and Astronomy: Retrospect and Prospect", Professor S. Chandrasekhar remarked that "the General Theory of Relativity is a theory of gravitation . . . and its natural home is in astronomy in the sense that its manifestations, whatever they may be, must be in the realm of astronomy." Again, no astrophysicist has made a greater contribution in propelling General Relativity to its ‘natural home’ in astronomy. Furthermore, just as Professor Whitehead had introduced a literary criterion to explain one of the consequences of the General Theory of Relativity as a contribution to the shaping of the concept of tragedy, Chandrasekhar has made use of the Bacon-Heisenberg aesthetic criteria in understanding the beauty of the framework of General Relativity. And in extending this argument, Chandrasekhar presents a bifocal view of the landscapes of Einstein’s General Relativity and Monet’s impressionistic paintings.

Professor Chandrasekhar has adorned Einstein’s "Natural home" — which is astronomy — with the landscapes of Relativistic Astrophysics and Monet’s Impressionistic Paintings. Actually the landscapes of General Relativity based on some mathematical structures, such as Chandrasekhar’s mathematical theory of black holes, the Chandrasekhar-Xanthopoulos field equations relating to the collision of impulsive gravitational waves and electromagnetic shock waves and the Subrahmanyan-Chandrasekhar-Valeria Ferari work on the non-radial oscillation of stars can be interpreted as an interplay of entropy, geometry and gravity. Similarly, Monet’s Series Paintings can be interpreted as an interplay of light, colour and aesthetics. Also, these paintings which range across the shimmering colours of the Haystacks, the beautiful patterns of the Poplars and the effects of Sunlight on the Foliage and Water, during the early morning at Argentueil near the Seine have been rightly described as the "Sistine Chapels of Impressionism". For these permutations and combinations of contoured beauty create different illusions of three-dimensional shapes in which the Haystacks, the Poplars, and the River Seine , can move, as it were, at different wave-lengths of aesthetic perception, thus reminding us of the art of Michelangelo in an Impressionistic world. And it is clear that just as matter implies gravity in a Relativistic setting, Chandrasekhar’s bifocal view of the landscapes of Relativity and Monet’s Impressionism reinforces the well-known scientific criterion that negative entropy implies creativity, scientifically as well as aesthetically.

Ananda Coomaraswamy’s theory of painting understood historically Leonardo da Vinci’s Holistic Theory of colour, interpreted artistically Newton’s Opticks, viewed mathematically Professor Raman’s holistic perception of colour, understood aesthetically Professor Bohr’s holistic theory of Complementarity also known as the Copenhagen Interpretation of Quantum Mechanics, viewed philosophically Professor Penrose’s holistic theory of physics, psychology and Neurophysiology, visualized mathematically Professor Chandrasekhar’s bifocal view of the landscapes of Relativistic Astrophysics and Monet’s Impressionistic paintings and, interpreted artistically, constitute a part of what Professor Robert Oppenheimer25 termed as "the life of the human spirit". Indeed, according to Professor Robert Oppenheimer,26 "An understanding of the complementary nature of conscious life and its physical interpretation appears to me a lasting element in human understanding and a proper formulation of the historic views called psychophysical parallelism . . . The wealth and variety of physics itself, the greater wealth and a variety of natural sciences taken as a whole, the more familiar, yet still strange and far wider wealth of the life of the human spirit, enriched by complementary, not-at-once compatible ways, irreducible one to the other, have a greater harmony".

No account of the interaction of colour with the elements — which explains how the varied colours in Nature arise from the diverse responses of the electrons in Matter to the different wavelengths of the incident light — will be complete without an assessment of Professor Gell-Mann’s contribution to the physics of elementary particles.

While reflecting on a theoretical framework into which the newly created particles could be arranged, Gell-Mann discovered that most of the particles could be classified as families or multiplets, which revealed geometrical patterns that were reminiscent of Lie groups. For these patterns had been originally worked out by a brilliant Norwegian mathematician Sophus Lie. Again when the Lie reasoning was applied to Particle Physics, it resulted in a new sophisticated theory which could explain not only the properties of the particles in the multiplets, but also predict the existence of new ones a la Mendeleev. Interestingly enough, Gell-Mann termed this theory ‘the eightfold way’ (named after the eight attributes of the Buddhist philosophical system) owing to the fact that some particles were grouped into families having eight members. This theory, also known as SU (3) Symmetry was independently formulated by an Israeli physicist Yuval Ne’ Eman. More importantly, Gell-Mann’s theory has been rightly compared with Dmitry Mendeleev’s celebrated classification of the Periodic Table of the Elements. And while arriving at this grouping, Gell-Mann defined a new concept known as the strangeness quantum number, S, which is linked with the multiplet charge.

Just as the Russian chemist Mendeleev had predicted the specific properties of the elements which would fill those gaps left by him in his Periodic Table, Gell-Mann predicted the properties of those particles which occupied those empty and pre-determined spaces in his classification. In fact, Gell-Mann’s theory was partly confirmed in the wake of the 1964 discovery of the Omega-Minus particle which had been predicted by him. Furthermore, Gell-Mann discovered that his theory could be explained by assuming that every strong interacting particle is derived from a triplet of particles, each possessing a fraction of a proton’s electric charge. Incidentally, the same discovery was made by an American physicist George Zweig at CERN — The European High-energy Centre of Physics near Geneva. Indeed it is the SU (3) theory which inspired Gell-Mann to visualize the existence of three entities out of which all the other particles could be constructed which he termed Quarks (the literary inspiration for naming these abstract mathematical concepts could be traced to James Joyce’s novel Finnegan’s Wake: "Three quarks for Muster Mark!"

As Heisenberg explained,27 "the conception of the objective reality of the elementary particles has thus evaporated in a curious way, not into the fog of some new, obscure, or not yet understood reality concept, but into the transparent clarity of a mathematics that represents no longer the behaviour of the elementary particles but rather our knowledge of this behaviour." For we encounter a world where the atomic quantum states have uniquely predetermined specific shapes and frequencies. Again, in order to grapple with certain statistical problems at the microscopic level, Gell-Mann had visualized colour as an ‘internal’, not observable, which is the famous Quantum Number in elementary particle physics. Furthermore, these hypothetically conceived fractionally charged quarks are found in six flavours — the up, down, strange, charm, top and bottom quarks — any one of which can be in one of the three colour states.

Although quarks have colour as an attribute, the physically observed particles (the baryons which are derived from three quarks and mesons based on a quark-antiquark pair) are regarded as colourless. And this concept of colour confinement has inspired a new discipline known as Quantum Chromo Dynamics which is based on abstract mathematics and indirect experimental evidence. Here one is reminded of the ancient Pythagorean idea of a "pre-established harmony". As is well-known, the Pythagorean view of the "harmony of the spheres" was based on the inherent symmetry of the celestial world of the distinguished from the terrestrial, made no sense in the Newtonian setting. However, the Pythagorean ambience of the "harmony of the spheres" can be understood in the context of Gell-Mann’s use of Quantum Numbers for the representation of quantum states. Indeed every hydrogen atom in the world strikes the same ‘chord’ (to use a Pythagorean expression) as visualized in the Balmer formula of spectral terms. In fact the Pythagorean "harmony of the spheres" undergoes a transformation as a vibration phenomenon of confined electron waves in modern particle physics. For the spectrum of frequencies of an atom reflects a typical set of values or rather the characteristic ‘chord’ of the atom, contributing to the re-emergence of "the harmony of the spheres" in the world of atomic physics. In fine, the ancient Pythagorean "harmony of the spheres" can be rediscovered, as it were, in the electron orbits of the atom which have triggered off the new Gell-Mann world of Quantum Chromo Dynamics.


1. C.V. Raman, Why is the Sky Blue? Lecture Community Service Centre, Ahmedabad (December 22, 1968).

2. Werner Heisenberg, The Representation of Nature in Contemporary Physics, Daedalus (1958).

3. N. Bloembergen, Reflections on Light, Raman Research Institute, Bangalore - 80 (1979).

4. S. Chandrasekhar, The Series Paintings of Claude Monet and the Landscape of General Relativity, Address delivered at the Dedication Ceremonies of the Inter-University Centre for Astronomy and Astrophysics, Pune (December 28, 1992).

5. Ananda Coomaraswamy, The Technique and Theory of Indian Painting, Technical Studies, Vol. III, No. 2, Fogg Art Museum, Harvard University, U.S.A. (October 1934), pp. 83, 88, 89.

6. C.V. Raman, The Physiology of Vision, The Indian Academy of Sciences, Bangalore (1968).

7. J.P. Richter, The Literary Works of Leonardo da Vinci, Oxford (1939).

8. A.N. Whitehead, Science and the Modern World, Mentor (1956).

9. Douglas Miller (ed. and tr.), Goethe: Scientific StudiesTheory of Colour, Part V, Suhrkamp Publishers, New York (1988) p. 272.

10. Ibid.

11. C.V. Raman, Nobel Lecture (1930).

12. C.V. Raman, "Anisotropy of Molecules", In Nature, London (1922).

13. C.V. Raman, "The Colour of the Sea", In Nature, London (1921).

14. C.V. Raman, On the Molecular Scattering of Light in Water and the Colour of the Sea, Proceedings of the Royal Society, London (1922).

15. S. Ramaseshan, "Introduction", to the Scientific Papers of Prof. C.V. Raman, In Colours and their Perception, Vol. VI, Indian Academy of Sciences, Bangalore, (1988).

16. David Malin, "A Celebration of Colour in Astronomy", In Current Science, Bangalore, Vol. 60, No. 1 (1991).

17. C.V. Raman, The New Physics, Philosophical Library, New York (1951).

18. Niels Bohr, The Unity of Human Knowledge and Essays 1958-72 on Atomic Physics, John Wiley, New York (1963).

19. C.V. Raman, The Molecular Diffraction of Light, Calcutta University Press (1922).

20. Roger Penrose, The Emperor’s New Mind: Concerning Computers, Minds and the Laws of Physics, Vintage, London (1990).

21. S. Chandrasekhar, How one may Explore the Physical Content of the General Theory of Relativity, Proceedings of the Yale Symposium in Honour of the 150th anniversary of the Birth of J. Willard Gibbs, The American Mathematical Society and the American Physical Society, (1990), pp. 227-51.

22. Ibid.

23. S. Chandrasekhar, Beauty and the Quest for Beauty in Science (July 1979).

24. The Role of General Relativity and Astronomy: Retrospect and Prospect, Invited Discourse at the Seventeenth General Assembly of the International Astronomical Union, Montreal, Canada, J. Astrophys. Astr (1980) 1, pp. 33-45.

25. J. Robert Oppenheimer, Science and the Common Understanding, Simon and Schuster (1953) pp. 80-82.

26. Ibid.

27. Werner Heisenberg, The Representation of Nature in Contemporary Physics, Daedalus, (1958).


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