THE DIAGRA DIAGRAM M OF VĀSTU PURUS A MAN D ALA: FROM MEANING TO MEASUREMENT Sanil. V
For the modern mind, the classical texts of Indian architecture could appear as mere construction manuals. The measurement and construction procedures given in the classical texts on architecture do not seek justification in a science or theory. They seem to be ‘appl ‘applie ied’ d’ from from the the very very begi beginn nnin ing. g. The The majo majorr text text on Indi Indian an architecture has the title Mānasāra, which means the essence of measurement.1 It would seem that, in India, we had a technology of archit architect ecture ure withou withoutt a scienc science. e. For us modern moderns, s, technol technology ogy is applied science. Some of the earliest modern studies on Indian archi archite tect ctur ure, e, by Ram Ram Raz, Raz, Jame Jamess Ferg Fergus usso son n and and Alex Alexand ander er Cunn Cunnin ingh gham am,, conf confiined ned thems hemsel elve vess to comp compar arat atiive and and 2 classificatory studies of building styles and ornamentation. They focused on the external shape and ornamentation and did not do justice to the status of a temple as a work of engineering or to the intellectual traditions behind it. There are several contemporary atte attemp mpts ts to manu manufa fact ctur uree a scie scient ntif ific ic basi basiss to ancie ancient nt Indi Indian an arch archiitect ecture, ure, by mixi mixing ng up astro strollogy ogy and and arch archiitectu ecturre. Astr Astron onom omic ical al cons consid ider erat atio ions ns were were very very impo import rtan antt in the the measurements of buildings. However, this does not warrant the postu postulat lation ion of any causal causal relati relations onship hip betwee between n the posit position ion of planets and human destiny. Most Most contemp contempora orary ry schola scholars rs avoid avoid naiv naivee aest aesthet hetic ic or scient scientist istic ic explanat explanation ionss of the measur measureme ement nt practi practices ces.. Ananda Ananda Coomaraswamy Coomaraswamy,, Stella Stella Kramrisch, Kramrisch, Subhash Kak and Kapila Kapila Vatsyayan follow an interpretative approach to architecture. For them them,, the the temp temple le is, is, at once once,, a symb symbol olic ic repr repres esen enta tati tion on of metaphysi metaphysical cal ideas and a realist realist representat representation ion of astronomic astronomical al data. This symbolism is effectuated through a web of astronomical considerations and does not seem to be grounded in any theory. Myth and metaphysics are expected to fill up this absence. The symb symbol olis ism m prov provid ides es the the fram framew ewor ork k for for a data data--fit betwee between n architecture and astronomy. Meaning guides measurement. The interpretative approach to the study of buildings seeks the inner meaning of architectural forms. A building is not merely a technological construct that serves a function, but a symbolic form that expresses meaning. From this point of view, ‘the Hindu temple is seen not only as a building providing shelter for the
Draft. Not to be quoted
image and the worshippers, but also as the image of the cosmos, the house of God and also his body, representing in its parts the drama of disintegration and reintegration, which is the essential theme of Indian myth and its ritual enactment in the sacrifice.’3
dala a la the key to Stella Stella Kramrisch Kramrisch made Vāstu Purusa Mand the the inte interp rpre reta tati tion on of the the Hind Hindu u temp temple le – its its meta metaph phys ysic ical al Vāstu Purus Purusa Mandd ala ala is a myth foundation. Vāstu myth-d -dia iagr gram am that that underl underlies ies tradit tradition ional al Indian Indian archit architect ecture ure,, especi especiall ally y that that of the temple. The knowledge of the construction and execution of Vāstu Purusa Manddala a la is part of the knowledge of architecture. The manddala ala is drawn on the levelled ground before the construction begins. It need not necessarily be a ground plan or site plan, or even coincide with the temple building. Vāstu means the planned site of the building. The purusa dala a la is a may be roughl roughly y interp interpret reted ed as the cosmi cosmicc man. man. Mand dala a la is a diagrammatic representation polygon. Vāstu Purusa Mand of the purusa drawn on the site and upon which the building stands. This diagram is square in shape and is further divided into square grids. The four cardinal points of the square correspond to the four directions. There are 8 cardinal points and corners of the intermediate directions. This is the natural division of the borders of a square. Repeated divisions of the borders can regenerate 32 squares on the border, each of which is associated with one of the planets and also with one of the leading stars of the house of the moon.
dala a la can be laid out in 64 or 81 squares. Both The mand these numbers are submultiples of the number 25920, which is the period of the precession of the equinoxes. It would seem that the manddala ala maps the cyclical movement of the sun and the precession of the equinoxes onto a square grid. dala a la is often studied at three levels. At the first The mand level it lays down the geometry of the building. The classical texts of Indian Indian architectu architecture re provide provide us with the relevant relevant measurement measurements. s. At the second level, these measurements reflect astronomical data. At the third level the temple is seen as a symbolic representation of dala a la symbolically links metaphysical and religious ideas. The mand the cosmos and the building, the inner and the outer, the earth and the heaven. ‘It is the intellectual foundation of the building, a forecast of its ascent, and its projection on earth.’4 According to Vāstu Purus Purusa Manddala a la regu Kramrisch, Vāstu regula late tess the the plan plan of the the building and makes the structure manifest the metaphysical idea.
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According to Kak, the Hindu temple represents both the outer and the inner cosmos.5 The outer cosmos is expressed in terms of various astronomical connections between the temple structure and the motions of the sun, the moon, and the planets. Here measurements of architecture directly represent or mirror astronomical facts. Kak gives several examples of our architects’ Pythagorean fascination with numbers. The number 108 is the average distance of the sun in terms of its own diameter from the earth; likewise, it is also the average distance of the moon in terms of its own diameter from the earth. The diameter of the sun is also 108 times the diameter of the earth, but that fact is not likely to have been known to the Vedic r si-s. The number of dance poses (karana-s) given in the Nāt ya-Śāstra is also 108, as is the number of beads in a rosary. The ‘distance’ between the body and the inner sun is also taken to be 108, and the number of marma-s in Āyurveda is 107. The total number of syllables in the R gveda is taken to be 432,000, a number related to 108. The total number of bricks in a Vedic fire altar is also 10,800. Kak notices the persistent occurrence of this number in the measurements of Angkor Wat temple. : 108 units measures the in-and-out circumambulation of the four corner towers together, the circumambulation of the central Visnu image from the three axial entrances, the inner axes of all four corner towers without images and the full vertical distance above and below the central sanctuary. The number 54 as half of the distance in sun- or moon-diameters to the sun or the moon is encountered at several places on the Western western bridge and the outer enclosure. [THIS LAST SENTENCE IS A BIT CONFUSING. CAN YOU MAKE IT A LITTLE CLEARER?] Some measurements indicate local astronomical data. In the Angkor Wat temple the door-to-door length of the north-south axis in the sanctuary is 13.41 cubits, which apparently represents the fact that the north celestial pole is 13.43 degrees above the northern horizon at Angkor. ‘... The west-east axis represents the periods of the yugas. The width of the moat is 439.78 cubit; the distance from the first step of the western entrance gateway to balustrade wall at the end of causeway is 867.03 cubit; the distance from the first step of the western entrance gateway to the first step of the central tower is 1,296.07 cubit; and the distance from the first step of bridge to the geographic center of the temple is 1,734.41 cubit. These correspond to the periods of 432,000; 864,000; 1,296,000; 1,728,000 years for the Kali, Dvapara, Treta, and Krita yuga, respectively. It has been suggested that the very
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slight discrepancy in the equations might be due to human error or erosion or sinking of the structure.’6 For Kak, the coincidence of the astronomical and architectural measurement finds its justification in the metaphysical ideas present in the Veda-s and Indian philosophy. The temple represents both the outer and the inner cosmos. The position of the gods in the Vāstu Purusa Mandala within the temple is a symbolic representation of the spatial projections of the cosmic purusa in his body. ‘The most impressive aspect of the temple representation is that it occurs both at the level of the part as well as the whole in a recursive fashion, mirroring the Vedic idea of the microcosm symbolizes (sic) the macrocosm at various levels of expressions. [PLEASE CHECK THE PRECEDING SENTENCE FROM THE QUOTATION: THERE SEEMS TO A PUNCTUATION AND? OR A WORD MISSING. ]This is done not only in the domain of numbers and directions, but also using appropriate mythological themes, and historical incidents. The mythological scenes skilfully use the oppositions and complementarities between the gods, goddesses, asuras, and humans defined over ordinary and sacred time and space.’7 The temple is the representation of the cosmos both at the level of the universe and the individual, making it possible for the devotee to get inspired to achieve his own spiritual transformation. The purusa placed within the brick structure of the altar represents the consciousness principle within the individual. Stella Kramrisch recognises the significance of the idea of measurement within the symbolic economy of the symbol. One of the names of the temple is vimāna where māna means measure. The purusa bears the measuring rod, knows division and thinks of himself as composed of parts. To measure is to bring into existence. That which can be measured is in the form of Umā, who is ‘measured out’ into existence. On its course, the architect’s activity measures the heaven. To measure is to create. However, Kramrisch hesitates from pursuing this line of interpretation and readily subordinates it to metaphysics. Measurement involves division and hence a corruption of the undividable. The work of Maya belongs to the order of māyā. ‘Vi-mana, measured in its parts, is the form of God which is this universe, the microcosm, and the temple as well, as a middle term made by man, the microcosm, according to his understanding and by measure.’8 Here the vimāna – the temple – becomes the middle term for the
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manifestation of the form of God. Measurement becomes the manifestation of a pre-existing order. Manifestation undergoes the necessary corruption of quantity and measurement. As we said earlier, Kramrisch notices that for our ancient architecture, as Protagoras too knew, man is the measure. This definition of man had acquired a certain anthropocentric interpretation in Renaissance Europe. However, for ancient Indians and also for the Greeks, this could have had a different meaning – that is, man as the bearer of measurement or measurement as creative and as belonging to the essence of man. Kramrisch avoids this possibility and drifts towards a humanist and symbolist interpretation of ‘man as measure’. She would read it as referring to a prior order existing in the body of man – the rhythm of breathing, the symmetry and proportionality of his body and the mark the cosmic order has left on him. Kramirsch proposes and then avoids a potentially subversive interpretation of vāstu – vāstu as residue.9 The place of the building is fixed by calculating the residue of the procedure of division. Vāstu is both residence and residue. However, she immediately appropriates it into the metaphysics of imperfection! The residue is the necessary imperfection that is the cause of creation: in the Indian tradition, the square, and not the circle which is a perfect sphere. However, according to Kramrisch, the square is privileged as the perfect figure of the imperfection without which the creation of the universe could not have happened. Kramrisch here avoids a more risky reading of the mandala in terms of the supplementary work of the residue, which would question the identity of the squares and the authority of the gods. Such a reading would have demanded that we see the relationship between the meaning and the building, the inner and the outer , or between the earth and the heaven, not in terms of resemblance but in terms of the real relations established by the supplementary work of the residue. The present paper is an attempt to explore a reading along these lines that could locate the generative potential of the Vāstu Purusa diagram beyond the symbolic domain. The interpretative approach, to a certain extent, accounts for the experience of the devotee, but it fails to throw light on how la regulates the technological act of the Vāstu Purusa Manda constructing the temple. The classical texts on architecture, as we said from the very outset, begin with the details of measurement and execution. Are they mere instruction manuals to be followed on scriptural authority? Most contemporary studies render the Hindu temple as a repository of astronomical information. This
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implies that ancient astronomy was a mere recording of facts. This collection of facts achieves its unity and inner coherence in the symbolic realm. On the one hand, the temple passively preserved and transmitted this factual knowledge and on the other hand, embodied myths and stories which in turn articulated metaphysical ideas. The unity of the temple was not technological, or even cosmological, but symbolic. Both positivism and interpretative phenomenology refuse the primacy of measurement. Measurement is made possible by a prior coordination between the systems of measurement and the world. Positivism sees this as a deductive link between theory and observation statements. For phenomenology, theory provides a prior explication of the object domain in which measurement takes place. ‘Measurement is ‘the essence of the procedures that allow objects of experience to be symbolically ordered according to a rule.’10 It converts experiences that have been interpreted in ordinary language into scientific data. It usually involves numbers, but it could also use other symbols. Measurement involves the technical operations on the basis of which objects are coordinated with systematically ordered symbols. The theory of measurement pre-explicates the relevant segment of possible experience. For example, the basic theoretical concepts of physics do not refer to any experiential world. The correspondence between the theoretical terms and experience is secured from the outset through a proto-physics that includes a theory of space, time and mass and also arithmetic. In this proto physics the rules for elementary operations of measurement appear as axioms. These axioms and the propositions derived from them express the idealised relationships of measurement operations in everyday life. In some cases, as in the social sciences, such a proto physics is in principle not available. Here the measurement techniques are constructed on a case-to-case basis, after the fact. In other words, the operationalisation of the theoretical terms is external to the theory itself. These operations are regarded as prestructured by symbolic interactions. This gives an epistemological priority to the interpretation of meaning over the measurement of data. In the place of a proto-physics, the social sciences can have a theory of culture. From the phenomenological perspective, the categorical framework of natural sciences, with the help of a theory of measurement, pre-explicates the world to suit the behavioural expectations of technological prediction and control, and presupposes a theory of culture that secures communicative
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interaction between scientists and also between scientists and the rest of the community. If epistemology is dissolved into a theory of scientific method, which in turn is pursued as a the sociology of science, then measurement in both natural and social science becomes a subject matter of a theory of culture. Thus, measurement is always already meaningful. As we have said, in India, measurement did not wait for justification or explication by theory. This leads the interpretative approach to develop a misplaced expectation that myths and narratives would fill in this gap and act as nascent theory. For them myths and stories are not mere fantasies. They embody or express metaphysical ideas. These ideas belong to the pre-understanding which structures the cultural life within which the measurement practices take place. Here measurement does not stand in a deductive but in a symbolic and interpretative relationship with the ideas expressed by the myth. Myths are the products of the idealising activities of the lived world. Here the question arises: In India, why did this idealising activity not reach the level of deductive geometry and remained at the level of myths? We can take one of the following options. If we accept the logical and teleological trajectories from primitive idealisations to the geometrical idea, then we may either take a Eurocentric view and hold that the birth of geometry was essentially Greek and account for its absence in India in terms of the historical delay in catching up. Or, we may conduct empirical research to unearth evidence for the availability of geometrical ideas in India. A more radical option is to question this logical and teleological narrative about the path that leads from pre-theoretical and primitive measurements to geometry. Roddam Narasimha explores this option and argues for two kinds of sciences – Western and Eastern -- which can be characterised by their distinct methods. The former is axiomatic and the latter computational. The West gave primacy to theory from which measurement followed deductively. Ancient Indian science followed the computational method, where observation and measurement did not find their justification in a prior theory. The task of scientists in India was to devise efficient algorithms that allowed computations that matched with observation. According to Narasimha, ‘The Indian sciences gave importance to computation and observation… Elaborate physical models and a process of deduction based on axioms are not seen as of great value; indeed the distrust of deductionist logic … appears to have been based on the conviction that the process of finding good axioms was a dubious enterprise.’11
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The Indian astronomers were not keen in formulating a picture of the heavens, or a basic model from which all can be deduced. They were searching effective methods of calculation that yielded the best predictions determined by observation. The goal of Indian astronomical calculation was dr g ganitaka, which literally indicated the identity of the computed and the seen. It is undeniable that in many areas Indians achieved enviable accuracy of prediction. According to Narasimha, in the nineteenth century, European astronomy quickly overtook Indian astronomy by synthesising the axiomatic and computational methods. Newton actually derived his results through a mixture of calculus and algebra, while concealing them under the dignified deductive procedure. The nature of the algorithmic law of gravitation is different from the deductive nature of the laws of motion. The former is not a law or hypothesis in the strict sense, but a particular proposition inferred from the phenomena. From this perspective, Newton was continuing the revolution Descartes had inaugurated by ‘algebraising’ geometry. Descartes wedded Greek geometry and the ‘barbarous art of Indo-Arabic algebra and algorithm’, preparing the way for Newton. The move to characterise science in terms of method and to account for cultural differences between Western and Indian Science in terms of methodological differences raises some serious questions. Is science a matter of method? Here we need not take the anarchic path of Feyerabend that rejects the very idea of a scientific method. The interpretative and phenomenological traditions too have insisted on not reducing sciences to a matter of method. Husserl argues that though Euclidean geometry is axiomatic, its origin or essence does not lie in any decision regarding method. Prior to such methodological considerations, geometry is born in a decision regarding the ideality of a geometric object. 12 According to Husserl, the emergence of axiomatic geometry is not a matter of the cultural choice of a method. It has a definite logical and teleological supremacy. However, the priority of axiomatic geometry is not a matter of its axiomatic method. It has to do with the constitution of geometric ideality. The measurement practices belonged to the pre-geometric or prescientific thinking. Geometrical idealisation has its basis in the pregeometrical sensible world and the practical arts of surveying and measurement. Even ancient societies had some ideas about
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countable numbers and measurable shapes. They generated abstract shapes out of the intuitively given surrounding world. Practical arts like surveying and measurement make use of these primitive idealisations, though they are tied to generally available empirical bodies. For Husserl, the imperfect idealisation in the ancient world is the trailblazer for pure geometry. The transition from life-world measurements to geometry was the event of the birth of a self-constituting subject of science. The origin of geometry does not lie in the discovery of new facts or the invention of a new method but in the original act of bestowing meaning on the geometrical object.13 This object has a pure and material ideality. It is pure in the sense that the geometric object is exhausted by its phenomenality. Geometry is a material discipline because, unlike the formal disciplines that work by stipulation, it follows pure intuition. The structure of the geometrical object has the structure of an infinitely open horizon where the original act of meaning-giving can be repeated infinitely. Thus, the geometrical object is the historical object par excellence. Henceforth, geometry can be pursued as a historical and cultural project. In other words, insofar as science is pursued as a historical and cultural project, Euclidean geometry has a privilege over pre-geometric measurement practices. The origin of geometry lies not in a methodological decision but in the emergence of a ‘we’. Or if the ancient Indians practised science as a historical project, then the Euclidean ideality is its inescapable telos. If the computational method was the mark of a serious difference then that should be accounted for in terms of the subject of science who practised that method. How do we imagine the subject of measurement differently? Can we describe the scene of the emergence of this geometric ‘we’? In which or whose history can we mark the origin of history? If this is the genesis of the structure, then what is the structure of this origin itself? What is the temporality of the origin of historicity? Answers to these questions are crucial for understanding the essential nature of the so-called algorithmic method of Indian sciences and measurement practices. At this stage I would pause for a moment to make a crucial methodological clarification. This study, which seeks to understand the relationship between theory and practice in ancient Indian architecture, does not rely entirely on ancient Indian texts on architecture or philosophy. Instead, it happily proceeds through Western texts and thoughts! This goes against the contemporary multiculturalist dogma that holds that technologies should be studied within their own cultural settings, and that those cultures in turn should be studied in terms of the beliefs and philosophical systems that are inherent to them. I reject this dogma not because I
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have confidence in any culture-independent and universalist intellectual foundation for technology. Instead, I hold that both the universalist and multiculturalist approaches have failed to account for technological practices in the West as well as in the East. My attempt is to use Indian architecture as a case to reveal this failure. The objectivist and interpretative approaches have failed to account for the relationship between measurement practices and Euclidean geometry. Those who claim to explore Indian architecture through the Indian texts merely repeat the legacy of this failure. In the rest of this paper I shall draw upon the work of Michel Serres, Santillana and Deleuze to suggest a new perspective to study technological practices and their relationship to science, culture and art. Only after developing such a perspective can we approach the Indian texts to throw light on the ancient Indian technological practices. Until then, both the practices and the discourses about them will remain as part of the case we are investigating. Michel Serres has examined the history of geometry without subscribing to the objectivist or culturalist paradigms.14 For him there is no logical or teleological hierarchy between the pre-geometric algorithmic practices and axiomatic geometry. Nor are these two mutually independent methods available for different cultures to choose from. He does not see a linear transition from pre-geometric measurements to geometric proofs and demonstrations. Between them he sees a bifurcation or branching off where each remains at once a sample of the other, and an impurity which prevents the other from closing in on itself. He arrives at this result studying the origin of geometry around a measuring device – the gnomon. The Greeks inherited it from the Babylonians. It is a shaft mounted on a plinth so that it casts shadows according to the position of the sun. According to Serres, the gnomon or sundial was not a primitive instrument to measure time -- a precursor to the timepiece. It was an ‘instrument of scientific research in its own right, demonstrating a model of the world, giving the length of shadows at midday on the longest and shortest days, and indicating the equinoxes, solstices and latitude of place, for example. It was more of an observatory than a clock .’15 It was both an observatory and a map of the world. The gnomon was an observatory, but it is not a precursor to the telescope. These two instruments belong to two distinct modes of knowing. The telescope belongs to a mode of knowing where the knowing subject projects the transcendental conditions of
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perception onto the world. It presupposes the eye of the viewing subject at the viewfinder ‘contemplating, observing, calculating, arranging the planets.’16 However, the gnomon exists prior to the invention of the subject. The role of the knowing subject too is exhausted in casting another shadow besides the gnomon. ‘ Modernity is born when this real world is taken as a scene and this scene controlled by a director, turns inside out – like a finger of a glove or a simple optical diagram – and plunges into the utopia of knowing, inner, intimate subject.’1717 The gnomon projects heaven on sand and is like a stylus through which the world writes itself. Here the world lends itself to be seen by the world that sees it. Modernity sees this writing ‘as merely the trailing edge of the projection of human knowing onto the world as observed and ordered.’18 For the ancient Greeks, knowledge was an event and the subject is just one part of it. The gnomon marks the passage from shadows to the sun that lies outside the subject. The knowledge shines at the tip of the gnomon. The figure of the gnomon can be extended to set squares and to tables and dictionaries. The gnomon works without the intervention of the subject and hence is an automaton. It encompasses both mechanical procedures and mnemonic devices. The experience of the world we receive through the gnomon is not filtered through a viewing eye or through a theory. Theoretical concepts and abstractions do exist. But they are found in the world. Theory does not occupy the role of a meaning-giving, perspectival standpoint. What intervenes is the gnomon that is a material object or a mechanical procedure. Thales compared the length of the shadows cast by the pyramid and gnomon and extracted the invariance. This inaugurates a third space of knowledge. However, it is the measuring device -- gnomon, which intervenes, discerns and decides not the subject. The algorithm, mechanical procedures tables and mnemonic devices are not inefficient instruments of a pre-scientific world, but material mediators between pre-geometry and geometry. Bruno Latour distinguishes these mediators from intermediaries.19 The latter links up those points that are separated by the ‘before’ and the ‘after’ of conventional temporality. The former confounds and complicates linear temporal paths. As a mediator, the gnomon would persist as a shadow within thea transparent objects[A WORD OR A PHRASE MISSING HERE] of geometry. They create what they link up. Latour locates these gnomonic mediators at all stages of the history of science.
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‘Around the work of the air pump we witness the formation of a new Boyle, a new nature, a new theology of miracles, a new scholarly sociability, a new society that will henceforth include vacuum, scholar, and the laboratory. History does something. Each entity is an event.’20 The mediators are not mere instruments but exploratory avenues. In the ancient world, astronomy grew without the aid of observing devices like telescopes. The act of discovery and the act of seeing did not occupy the same place. ‘In the diagram of the sun at the source of light of the shaft and the image on the ground there is no place for the eye, no position which we can call a view point.’21 Serres depicts the transition from the pre-geometrical age to the geometric age through a drama in two acts. The first act consists of a scene that we have already seen. Thales stands in front of the pyramid and compares the length of the shadows cast by the pyramid, him and the gnomon. The second act consists of Socrates, Plato and Meno where Socrates demonstrates that the slave boy could prove Pythagoras’ theorem. The gnomon casts its shadow on this scene too. However, Socrates wants Meno to look beyond the shadow towards the unseen diagonal that again is a shadow but lodged in his memory. This scene announces a turning point in the history of geometry, where Socrates finds holes in the algorithmic thinking of the slave and clears the ground for axiomatic thinking. However, this is not a change in method. From the world of ratios and tables we move to the world of the unseen diagonal. The world we can measure borders on another world that is infinitely remote. Socrates draws us to this world where ideality is subtracted to the point of exhaustion from all apprehension. The abstract idea lies at the heart of this abyss. This is also the space of the thinking subject. Here geometry needs a subject who can demonstrate by drawing lines on the sand. It also opens up a space of knowledge which is away from that of human relations. Nature no longer writes on its own. Knowledge needs a subject that can stand in relation to another space that is outside the world in which it lives. ‘There is something of the transcendental in Euclid’s beginnings which echo the beginnings of geometry or which express and continue them; there is something of the conditional there, of the elementary to be precise. But they do not lie in the subjective or in the a priori, nor in the formal or in the pure, in the Cartesian or Kantian senses. They reside in the world, Sun, Earth,
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in the artificial, shaft, table, compass, ruler, statue, in short in the community.’22 The Euclidean axioms describe conditions in the thought of establishing a community which relates to an objective world that transcends its relations. In the ancient world the numbers quantified human relations. No known problem of measurement was about nature. Numbers regulated taxes, commerce and earnings. Geometry interrupts this and begins to measure objects. Serres, unlike Husserl, does not recapitulate the transition from measurement to geometry from the standpoint of the subject. He shows its origin in the gaps or vortexes of the subject-less science of pre-geometric measurements. Gnomon offers the grid through which the subject emerges. The pyramid, gnomon and the human figure are not mere objects for the application of algorithmic or axiomatic methods. They are mediators or transition points between the two scenes of knowledge. They are ambiguous moments between forking temporal trajectories and hence the conditions which make geometry both possible and impossible. The future of geometry shall remain open. However, the structure of this opening remains embedded in the earth that bearsore the shadows of men, tombs and gnomons. Hence the future of geometry is inconceivable without it being corrupted by algorithms and techniques. That will not deter the puritans from constantly trying to re-establish the pure ideality of geometry. The pursuit of that ideal object would demand more and more mediators and synthesis, leading to the proliferation of algorithms and gnomons. A history from the shadow of the gnomon shows that geometry does not have a unified temporality or sense of history and that it is animated by multiple temporalities, rhythms and vortexes. Now we can begin to locate the place of the Indian building on the plane of knowledge. The temple or house is not merely an object with parts having stipulated measurements. Nor is it a construction that can be exhausted by an analysis into ideal geometric forms. It also not applied astronomy. The temple is more of a gnomon – an observatory and a map of the world. Myth too belongs to the same plane as gnomic devices that put to work mechanical reproduction and mnemonic techniques. Before becoming stories, myths are part of measurement technology. Myths are not narrative justifications for measurement. They are measuring devices/operations themselves. To see this, we must break free from the interpretative views on myth that
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misunderstand the latter as symbol and as compressed or indirect meaning. Myth should be studied on the plane of science itself. Giorgio De Santillana’s Hamlet’s Mill is an initiative in this direction. It claims that myth is a language for the generation and perpetuation of astronomical data. He studies a specific myth – the Hamlet’s Mill, which encodes data on the precession of equinoxes. Why does this data take the form of myth? Santillana rejects two common approaches to the myth. One of these views holds that the ancients were scared by the celestial events and took recourse to myth to deal with their fear. The second view, which Santillana contemptuously calls the ‘fecundity-trust’, sees myth as part of the fertility rituals. The former sees myth as failed science and the latter as misguided technology. However, both these approaches see myth as an attempt to make sense of natural phenomena. However, making sense may not be the only, or a properly human, response to events. ‘One should pay attention to the cosmological information contained in ancient myth, information of chaos, struggle and violence. They are not mere projections of a troubled consciousness. They are attempts to portray the forces which seem to have taken part in the shaping of the cosmos. Monsters, Titans, giants locked in battle with the gods and trying to scale Olympus are functions and components of the order that is finally established. A distinction is immediately clear. The fixed stars are the essence of Being, their assembly stands for the hidden counsels and the unspoken laws that rule the whole. The planets seen as gods, represents the Forces and the Will.’23 We are familiar with the humanisation of nature where ancients ascribed human-like personalities to trees and gods. We also have the Feuerbach thesis that in the god man externalises his own powers. However, myth addresses the time when substance itself was thought to be god. This is the time when the godhood of gods was conferred on them. Later, these gods were seen in human or animal forms. Myths offered a schema or technical language for the divination of the substance. This does not mean that mythmakers believed that substance was like gods. In fact, the idea of beliefs makes sense only after the gods are in place. Myth had nothing much to do with beliefs. ‘Myths can be used as a vehicle for handing down solid knowledge independently from the degree of insight of the people who do the actual telling of stories, fables etc.’ 24
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According to Santillana, myth is knowledge about cosmological events. This knowledge is generated and transmitted without involving the subjective conditions of the knower. What does it mean to represent an event? For us, it involves bringing it under the subjective conditions of space and time. This makes the event into a historio-geometrical fact. The ancients had a different relationship with the event. It is not that the precession of equinoxes threatened the immature science of the ancients forcing them to invent some escapist explanation. They had a cognitive grid that could register barbaric events. To represent time means to set up a theatre in which space and time can emerge as characters. This drama stages the very birth of the subject endowed with a sense of history and culture and science. The characters in the mythical narratives are functions of time. They are not persons or things. The language of time used in myth does not address a world of spatially localisable objects. Time of the myth is not historical time. The historical time or narrated time is caught in the aporia of the time that passes and the time that is always present. In history we encounter events with the surprise of fait accompli – like Auschwitz. Mythical time is always conserved – mostly by the structure of cycles. In the mythical world, space is the locus of indefiniteness, incoherence and unruliness. Since Kant, we know that we can have only an indirect representation of time.25 Time is a condition for representation and cannot be brought to direct representation. It is forever caught in the enigma of the passing present. Narratives, not myths, make positive use of this enigma to provide us with an indirect representation of time. Time becomes the inner sense of the representing consciousness and merely indicates that the connections established in the world of disconnected objects are congenial to the consciousness that made those connections. Against this, myth conserves an archaic past which has never been made present.26 ‘All that is living reality, sub specie transeuntis, has a tale, as it appears in awesome, or appalling, or comforting aspects, in the “fearful symmetry” of tigers or theorems, or stars in their courses, but always alive to the soul. It is a play of transmutations which includes us, ruled by Time, framed in eternal forms. A thought ruled by Time can be expressed only in myth.’ 27
15
Myth is ambiguous and allows a plurality of narratives. But this does not mean that it anticipates and explores an order in the fictional dimension. It is not the stories themselves that maps time but their affect – being appalling, comforting, fearful. This affect is a play of transmutations that include us too. This subjects us to a radical passivity which goes beyond the unity of the microcosm and macrocosm. In myth we are absorbed into the play of transmutations. As the archaic thought of Anaximander recognised that ‘the source from which existing things derive their existence is also that to which they return at their destruction, according to necessity; for they give justice and make reparation to one another for their injustice, according to the arrangement of time.’28 This time will remain inscrutable to both psychology and cosmology. Time is the number or measure of movement, provided that this movement is a transmutation, play and dispensation of justice from which existing things receive their existence. Myth is measure.
Vāstu purusa manda la is a mythical diagram not because it depicts some mythical character. Myths need not always be in the language of words. This is a myth as a diagram. Again this does not mean that the picture of some mythical character is waiting to be liberated into a verbal language. Diagramaticity belongs to the essence of myth. Perhaps the diagram refers to a level of language specific to myths, gnomons, tables and algorithms. I shall borrow the idea of diagram from Deleuze who used it in a totally different context – in the study of the paintings of the British painter Francis Bacon.29 However, at the outset, let me point out what would seem like a superficial similarity between Deleuze’s idea of diagram and the diagram we are studying. la was part of the preparatory rituals of temple Drawing the manda building. Deleuze’s diagram too is the formal structure of the preparatory work the painter does before the act of painting. Before we pursue Deleuze’s idea of diagram, let us point out the difference between a diagram and a picture. Take the diagram of an experimental set-up or the circuit diagram of an electronic device. This is not a pictorial description of what the text describes. A mere description is not enough to get our acts together. A photograph of the experimental set-up also is inadequate. The circuit diagram of an electronic device is not a sketchy version of the photograph. The diagram is meant to allow operational interventions. The diagram pictures the set-up as something to be made or to be worked upon. We may say it is an operational representation made up of practical or manual traits. Following Wittgenstein, I would say that the proposition and
16
picture state or present facts whereas the diagram opens up possibilities of fact. The diagram intervenes and disturbs the conventional exchanges between blind words and mute pictures. Deleuze deploys the concept of diagram to go beyond the idea of a symbolic code and hence the order of symbolic meaning. The diagram is not a code. It is an operative set of asignifying marks, traits, lines or colours. It disturbs or erases the figurative givens on the canvas or the intentional content of what one wants to paint or say, so that something new can emerge. It is at once chaos and order. It unleashes subversion locally while preserving the appearances globally. Diagram always stays within the order of language though it works by an analogical use of discursive language. As we have said, many interpreters of Indian architecture read the temple in terms of the analogical relationship between microcosm and macrocosm, the divine and the human, and the heaven and the earth. For them this analogy follows a symbolic code provided by Hindu religion and metaphysics. We get a very different picture if we replace the symbolic code with diagram as la speaks the form governing the analogical relations. The manda an analogical language. An analogical language is a language of relations. Myth too uses a language of relations. The word has no density of its own. Instead of being the sign of a thing it exhausts itself in conveying a connection. Often we think that analogy works with some immediate evidence and hence does not need a code. This is not correct. What such a language brings into relations need not have any obvious resemblance. Here lies the difference between a picture and a diagram. A picture is produced by resemblance. But the diagram produces resemblance. A diagram consists of non-representative, non-illustrative, nonnarrative marks or sounds. Relations to be reproduced are produced using completely different and non-resembling relations. The mandala does not map heavenly bodies to their look-alikes on earth. Instead it produces those relations which need to be reproduced on earth. Building construction becomes astronomical research pursued through other means. Resemblance here is not produced symbolically, but practically. Let us see how the diagram works. In the 1946 painting, Bacon set out to draw with the idea of a bird alighting on a field. But suddenly the lines took independence and configured themselves into a man with an umbrella. The diagram is a set of procedures that enable the transformation of the bird into a man with the umbrella. This is not a transformation from a bird form to
17
an umbrella form. If it were, such a transformation would privilege optical resemblance and hence the eye. This transformation is not based on any visual resemblance between the two forms. We can’t say how some part of the umbrella resembles some part of the bird. However, it is indeed possible for us to trace our hand over the bird picture or rub it or wash it with colours and say ‘here is the umbrella’. So there is a correspondence or resemblance between aspects of the intentional figure of the bird that the painter started with, and the whole of the figure which has dawned upon the canvas. This resemblance is not an optical relation between the look-alikes. It is a set of real relations that constitute a space of objective indiscernability. The diagram is the work of a hand that effectuates these real relations. This hand-work which moves through the space of real relations is called scrambling. The diagram scrambles the figurative form of the bird and substitutes it with non-figurative traits of the bird from which another – the umbrella -- emerges. This scrambling is not g uided by resemblance but produces it. Diagram brings chance to the painting. It scrambles the unity of the visual form and thus brings chance to the canvas. Looking at a diagram is like looking at a graph or an xray. They are objective representations because the diagrammatic scrambling undoes the filters of theory or consciousness and prepares the opening for a chance encounter with reality. Narrative is the classical means to transform discordant events to concordant actions. Diagram is the means for transformation in the opposite direction – action to event. The scrambling operation of the diagram destroys the lived unity of action and allows the emergence of a new form of life – the event. In this sense the diagram is a direct time image. The temple is not a technological artefact constructed through the application of a science. Nor is it a repository of cultural symbols. Also, it is not an indirect representation or symbol of the cosmos. It is an intermediary and the time frame for the creation and transmission of the knowledge of events. Measurement as a preparatory operation scrambles beliefs and actions to release events. The metaphysical ideas were perhaps the result and not the source of measurement. Protagoras was right – man is the measure. It does not mean that he is the subject who sets the standards. Such a conception belongs to us moderns. For the ancients, man’s being might have been essentially diagrammatic. Man is the measure. He fell from the heavens. Upon his shadow rose tombs and temples.
Notes:
18
19
Prasanna Kumar Acharya, Architecture Books, 1980). 1
of Mānasāra, Mānasāra Series (New Delhi: Oriental
See Ram Raz, Essay on the Architecture of the Hindus (Varanasi: Indological Book House, 1972); James Fergusson, On the Study of Indian Architecture (Varanasi: Indological Book House, 1977); and Alexander Cunningham, The Stupa of Bharhut (Varanasi: Indological Book House, 1962). 2
3
Pramod Chandra, 33. 4
On the Study of Indian Art (Cambridge: Harvard University Press, 1983), p.
Stella Kramrisch, The Hindu Temple , Vol. 1 (Delhi: Motilal Banarsidass, 1976), p. 17. Subhash Kak, ‘Space and Cosmology in the Hindu Temple,’ paper presented at Vāastu
5
Kauśal : International Symposium on Science and Technology in Ancient
Indian Monuments, New Delhi, 2002. 6
Ibid. p. 3.
7
Ibid.
8
Kramrisch,
ed. cit., p. 132.
9
‘The very imperfection which is the cause of the existence of the world serves as the basis of all astrological forecasts and astronomical calculations. There is always a remainder. For nothing could continue if nothing were to remain. The space occupied by anything in the present, is in the residue of the past. The name of v āstu derived from vastu, a really existing thing, signifies residence as well as residue.’ --- Kramrisch, ed. cit., p. 37. ‘The remainder or residue is that which remains or subsists when everything else has come to a conclusion. If something is complete in itself, perfection, nothing is left over, there is an end of it. If there is a remainder there is no end to it. So the remainder is the germ and material cause for what subsists. It is the concrete reality of a thing.’ – Ibid. p. 45. Habermas Jurgen, On the Logic of the Social Sciences , trans. Shierry Weber Nicholsen and Jerry A. Stark (Cambridge: Polity Press, 1988), p. 96. Proper reference of quote needed. 10
11
Roddam Narasimha, ‘Axiomatism and Computational Positivism: Two Mathematical Cultures in Pursuit of Exact Sciences,’ in Economic and Political Weekly , Vol. XXXVIII (2003): 3671. 12
For an account of Husserl on the origin of geometry, see Sanil. V, ‘Mathematical Idea and Cinematic Image,’ in Economic and Political Weekly , Vol. XXXVIII (2003): 3657-3661. 13
Since Roddam Narasimha understands Western geometry in terms of axiomatic method, for him, Descartes was synthesising pure deduction with an alien computational method. Newton was the culmination of this effort. However, Husserl sees this differently. For him, Descartes was liberating the geometric essence of algebra and also freeing geometry from being bound by the limitations of the tangible dimensions of the physical world. Reflection of method was crucial for Descartes but the question of method was subsumed under question about certainty. With Galileo, method loses this epistemological value. Paradoxically this led to the proliferation of methods, techniques and algorithms. Science becomes a matter of method and techniques precisely when epistemology is dissolved into a study of the empirical history of science. For Husserl this is not a synthesis but a contamination of the pure essence of geometry. It marks the technicisation of science and the forgetting of the original task of Western science. The impurity is not the Indian algorithmic method but the historical predicament of the very question of method coming to dominate the character of science.
Michel Serres, ‘Gnomon: The Beginning of Geometry in Greece,’ in A History of Scientific Thought : Elements of a History of Science , ed. Michel Serres (Oxford and Cambridge, Mass.: 14
Blackwell Publishers Inc, 1995). 15
Ibid. p. 79.
16
The quote needs to be referenced.Ibid
1 17
Ibid p.80
18
Ibid.
19
Bruno Latour, 1993), p. 79.
We Have Never Been Modern (Cambridge, Mass.: Harvard University Press,
20
Ibid. p. 81.
21
‘Gnomon: The Beginning of Geometry in Greece,’ p. 86.The quote needs to be referenced.
22
Ibid. p. 117.
Gioggio de Santillana and Hertha von Dechend, Hamlet’s Godine Publishers, Inc., 1977), p. 151. 23
24
Mill (New Hampshire: David R.
Ibid. p. 312.
25
Sanil. V, ‘Time Passing: Kant Goes to Movies,’ in Indian (2004).
Philosophical Quarterly 13.1-4
26
For the interpretative approach, myths are compressed and disguised meaning. It is a symbol which hides more than it reveals. I agree that myths , like dreams, are invitation to interpret and narrate. However, they are not essentially intentional and symbolic constructions waiting to translate into words and stories. Rarity or poverty of meaning marks the myth. Myths are sites of distortion of meaning just as rituals are sites of gratuitous violence. 27
Santillana, ed. cit., p. 47.
Hermann Diels, Ancilla to Basil Blackwell, 1948), p. 19. 28
the Pre-Socratic Philosophers , trans. Kathleen Freeman (Oxford:
Gilles Deleuze, Francis Bacon: Continuum, 2003), pp. 93-110. 29
The Logic of Sensation, trans. Daniel W. Smith (New York:
