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A novel application of statistical analysis probes the mysteries of sculptures dating from the seventh and eighth centuries A.D.

The Indian subcontinent abounds in exquisite stone carvings and sculptures, some dating from the pre-Christian era. In the southernmost part of India, the earliest of these works were carved during the Pallava dynasty of the seventh and eighth centuries A.D.

Ancient and medieval Sanskrit texts ... include instructions for painting, sculpting, and creating painted carvings.

These sculptures, located near Madras, have no parallel in artistic quality anywhere in India. This article describes our pioneering work in computer-aided analysis of such work¹.

The Pallava kings ruled from the city of Kanchipuram, and their chief port was Mahabalipuram. They built many palaces, and they carved many temples out of solid rock; only the temples have survived. Most of the Pallava temples at Mahabalipuram were carved in hard rock {Figure 1) and those at Kanchipuram in softer sandstone.² The most famous monument at Kanchipuram is the Kailasanatha Temple (Figure 2).

Sanskrit inscriptions on the Kailasanatha Temple attribute it to King Rajasimha, the Lion King, who ruled from about 700 to 720 A.D. Carvings on the temple (see Figure 3) represent human as well as divine figures in different stances. Unlike Greek and Roman sculpture, Indian sculpture does not show musculature. Except for Gandhara art, which was influenced by the Greeks, dress in Indian art is not depicted with heavy folds. Often just a line is shown to indicate the edge of a garment. Weapons and other emblems are shown just above the hands or held gracefully. Natural flexions of the human body are shown, along with different hand poses or gestures. Each gesture has a specific meaning.

Figure 1. Five rathas, or chariots, carved in hard rock at Mahabalipuram. Each monument is in fact a temple, but according to legend they are chariots of the Mahabharata War, turned into stone.

Ancient and medieval Sanskrit texts called silpa sa$stras, or art manuals, contain information on architecture, temple rituals, iconography and iconometry.³ They include instructions for painting, sculpting, and creating painted carvings. Their canons prescribe that the length of the face should be 12 angulas (an angula is a proportional unit equal to the width of a finger), and they also prescribe the length and breadth of the nose. eyes, and lips. It is generally believed that such texts guided the sculptors who carved the Kailasanatha Temple.

To compare different figures on the temple, we took facial measurements from each carving using calipers and other anthropometric instruments. All measurements were standardized by reckoning the length of the face to be 12 units, corresponding to the 12 angulas of the canons. We compared our measurements mainly with the canonical proportions prescribed in the Silparatna (silpa, sculpture or painting; ratna, gem) and the Ka$syapa Silpasa$stra (the K$a$syapa art manual),

Using principal component analysis, a statistical technique for reducing dimensionality in multivariate problems, we represented each sculpture in terms of ten variables denoting different facial proportions (see Table 1). With input consisting of data from about 40 sculptures, we used a computer to standardize the measurements and find average values.⁴ Since the face length was reckoned as 12 units for all the sculptures, the ten original variables were reduced to nine. The calculations involved inverting a 9-by-9 matrix. We wanted to discover whether the nine variables could be replaced by fewer than nine components, each component being a linear combination of variables.

Figure 2. The Kailasanatha Temple, a structural temple built at Kanchipuram by King Rajasimha.

    Our computations produced five principal components, but each component could account for  only 10 to 27 percent of the variability. If Rajasimha's sculptors had strictly followed any of the common canons based on the angula, one would expect, from a theoretical point of view, that the first principal component would account for most of the variability since the different facial proportions are all directly proportional to a single unit, the angula. The surprising finding that they had not closely followed the canons led us to examine the sculptural proportions in greater detail.

Figure 3. Female figure carved in sandstone of the Kailasanatha Temple.	Figure 4. The face of a maiden with the long nose and long, narrow eyes characteristic of the Rajasimha period.

Table 1
 Canonical values of facial proportions from the Silparatna and average values of measurements made on sculptures of the Pallava period in southern India. All values are in angulas (see text)

KM Krishna Mandapa        AR Arjuna Ratha          VC Varaha Cave

DR Dharmaraja Ratha        AC Adivaraha Cave       TC Trimurthi Cave

Facial proportions

We found that the facial proportions of the Kailasanatha carvings (Figure 4) are distinctly different from those prescribed in the canons (see the first two columns in Table 1). They are also different from those of a typical human face. For male figures, the canons prescribe that the length of the forehead, the length of the nose, and the nose-to-chin distance be equal. However, the face on a typical Kailasanatha carving has an extraordinarily long nose and a short nose-to-chin distance, with hardly any space between the nose and the lips, and also long, narrow eyes.

If the artisans of the Kailasanatha Temple did not follow the canons, on what did they base their proportions? They certainly did not base them on a typical human face. Furthermore, artisans of the next generation did not use the same proportions. It is quite possible that the Kailasanatha sculptors were inspired by the face of a particular Pallava queen, but that this ideal went out of fashion after her death. It is also possible that the sculptors who created the temple migrated, afterward, to some other kingdom.

Figure 5. The Shore Temple, a structural temple built near the sea by King Rajasimha.

Figure 6. A cave temple at Mahabalipuram, carved out of solid rock.

It is known that King Rajasimha built a structural temple at Mahabalipuram, commonly known as the Shore Temple (Figure 5), in which the sculptures have features similar to those on sculptures in the Kailasanatha Temple. However, other sculptures at Mahabalipuram, on rock-cut cave temples (Figure 6), bas-reliefs (Figure 7) and the monoliths shown in Figure 1. have facial proportions that are distinctly different from those of the Rajasimha period. They do not have extraordinarily long noses, and their eyes are less stylized. Some authorities believe that Rajasimha commissioned these other sculptures as well; others believe, on the basis of inscriptional evidence on the sculptures, that they may have been carved as early as 650 A.D.

In an effort to resolve this controversy, we measured the facial proportions of carvings on a number of monuments at Mahabalipuram. Figure 8 shows a portion of one of them, known as the Penance Panel. We found that the measured proportions differ from both the canonical proportions and the Rajasimha proportions measured at the Kailasanatha Temple (see Table 1). In particular, the noses are longer than the canonical prescription (4 angulas) but not as long as the typical nose of the Rajasimha period (5.4 angulas). Moreover, the eyes are not as long and narrow as those in typical Rajasimha carvings. These findings support the theory that most monuments in Mahabalipuram are of the pre-Rajasimha period.

Costumes and jewelry

To support the iconometric evidence that the Mahabalipuram monuments do not belong to the Rajasimha period, we looked for other kinds of evidence. Costumes and jewelry of any period can be used to date sculptures and monuments with reasonable accuracy.⁵ Firmly dated sculptures of the early seventh century have huge ear ornaments, with diameters exceeding 5 angulas, and the ornament on one ear differs in shape from that on the other ear. Crowns are of moderate height, about 15 angulas. During that period, queens and princesses went bare above the waist, their bodies painted yellow with sandalwood paste, and female guards wore ornamental breast bands (see Figure 9).

Figure 7. Close-up of a carving on the Penance Panel, a magnificent bas-relief at Mahabalipuram.

Figure 8. A view of the Penance Panel at Mahabalipuram, showing the dress and ornaments of the pre-Rajasimha period.

Figure 9. Female warrior of the pre-Rajasimha period in a cave temple at Mahabalipuram. Note the absence of vertical straps on the breast band.	Figure 10. A prince and princess as depicted on the Arjuna Ratha, near Mahabalipuram. The large ear ornaments and the facial proportions are typical of the pre-Rajasimha period.

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There were many changes in fashion during the following decades, and by the end of the seventh century a different style had emerged. This new style was in vogue during the reign of Rajasimha. Ear ornaments became smaller and were the same on both ears. Crowns were unusually tall, more than 30 angulas hightwo and a half to three times the length of the face. Vertical straps appeared on breast bands. Men started wearing anklets. The undated sculptures of Mahabalipuram, such as the prince and princess in Figure 10, have large ear ornaments and crowns of medium height, and female guards have breast bands without vertical straps. Therefore most of the Mahabalipuram monuments must be of the pre-Rajasimha period.

Canons, carvings, and humans

To establish comparisons, we analyzed nineteen sets of canonical proportions, ten carvings of the god Siva⁶ in a sitting posture, and facial and anatomical proportions of fifteen men students at Madras Christian College in the same sitting posture. We made four facial measurements and five body measurements for each of the students, who ranged in age from the late teens to the early twenties. Six of the Siva carvings were measured at Mahabalipuram and four at Kanchipuram. We used cluster analysis⁷ to make a computer study of the canons, carvings, and human subjects, representing each object in terms of nine measurements.

Figure 11. Dendrogram showing results of cluster-analysis studies of canons, carvings, and human subjects. Note clusters of symbols representing canonical proportions and measured proportions of students. The Euclidean distance between points representing a pair of objects is shown by a pair of vertical arms connected by a horizontal line. The longer the arms, the greater the Euclidean distance between the objects represented by the end points. Circle: Siva-Mahabalipuram Circle-solid : Siva-Kanchipuram Triangle: Canons Triangle solid: Students

In cluster analysis, which is used for discovering related groups or clusters within complex data,^8,9  calculations involve comparison of objects pair by pair. For a set of, say, 50 carvings, 1225 comparisons are made and the Euclidean distance is found in each case. The Euclidean distance is a mathematical distance between two points in an n- dimensional space. In our problem, each object is represented as a point in the nine-dimensional space formed by the nine variables. The more alike two objects are, the shorter the Euclidean distance between the points representing them. The calculations can be done in seconds with a computer, and the results can be plotted in the form of a dendrogram, a diagram in which points representing similar objects are clustered together.

The dendrogram showing our results is reproduced in Figure 11. Most of the Siva carvings from both Kanchipuram (solid circles) and Mahabalipuram (open circles} are of the Rajasimha period and are clustered near the right end of the x axis in Figure 11, but one from Mahabalipuram of the pre-Rajasimha period stands out clearly at the extreme right. Another Mahabalipuram carving, symbolized at the extreme left, also belongs to the pre-Rajasirnha period and is closer to human and canonical proportions (represented by solid and open triangles, respectively). The measured proportions of the students (solid triangles} are more or less similar, forming a cluster near the middle of the x axis. The one exception, near the right end of the x axis, is a student with an unusually small face, which stands out because the proportions are based on face length.

Figure 12. The Dharmaraja Ratha, tallest of the five monoliths shown in Figure 1.It is covered with more than 50 carvings.

Three types of canonical proportions emerge from the cluster analysis. Seventeen of the nineteen sets that we analyzed form one cluster in Figure 11, even though the proportions are given different names in different canons. The two remaining types form singleton sets near the right end of the x axis and probably represent the works of two sculptors from the southern school. It is surprising that the main cluster contains sets of proportions with different names from different texts. The different names imply that the proportions represent different types, but their clustering shows that they were in fact based on a single type. In the late medieval period, that type must have replaced the different types of proportions prescribed in the early canonical texts.

Chariots in stone

At Mahabalipuram there is a unique group of five monolithic temples which, in popular imagination, are five chariots left behind by the heroes of the Mahabharata, one of the great epics of ancient India. The largest and most magnificent of the monoliths is the Dharmaraja Radha, the chariot of Dharmaraja¹⁰ (Figure 12), which belongs to the pre-Rajasimha period. We took measurements of more than 50 carvings that adorn this temple.¹¹ The average values found by computer analysis reveal that the facial proportions are distinctly different from those of a typical carving of the Rajasimha period (see Table I).

We wanted to determine whether all or most of the sculptures were executed by a single artist, or whether perhaps each was executed by a different artist. These questions are important in determining how long it took to carve the monument. If each carving was done by a different sculptor, the work could have been completed within a year or two. On the other hand, if a single artist executed all or even most of the carvings, the sculptural parts alone would probably have taken about ten years to complete.

Figure 13. Carving of the sun god Surya in the Dharmaraja Ratha, with the halo only partly finished.

Figure 14. Representation of a king in the Dharmaraja Ratha, with the feet left unfinished. The Sanskrit inscription above the figure is also unfinished.

Figure 15. Adjacent carvings of the god Siva in the Dharmaraja Ratha, probably both done by the same artist.

Figure 16. The god Vishnu as depicted in the Dharmaraja Ratha, probably by the same sculptor represented in Figure 15.

The Dharmaraja Ratha has three floors, and there are unfinished sculptures on each floor. For instance, on the top floor, the halo of the sun god Surya is only half finished (see Figure 13). On the ground floor, the feet of a king and the Sanskrit inscription above the sculpture are unfinished (Figure 14). The presence of unfinished sculptures on each floor convinced us that more than one artist had worked on the monument. We then looked for carvings created by the same artist. On the eastern wing of the southern face of the middle floor are adjacent representations of Siva with identical faces (Figure 15), indicating that they must have been the work of the same artist. Using a hundredth of an angula as the unit of measurement, we found, again with the aid of computer analysis, that the Euclidean distance between points representing the two faces is only 15 units. We attribute common authorship to any carvings that have such a high degree of similarity. A representation of the god Vishnu on the same floor (Figure 16) is only 10 units, in Euclidean distance, from the Siva sculptures, suggesting that the Vishnu was carved by the same artist as well. On a similar basis, we found 26 figures that were carved by the same artist. These carvings formed a cluster in the computer analysis. The maximum dissimilarity we found between two figures created by the same artist in the Dharmaraja Ratha is in a beautiful panel of Siva and a devotee on the northern side of the middle floor. Siva's arm is around the shoulder of the devotee. The figures are certainly the work of the same artist, yet the difference in facial proportions, in terms of Euclidean distance, is 50 units.

Summary

We have used computer methods to answer many interesting questions in Indian art history. With reference to the Pallava monuments of the seventh and eighth centuries, we determined the average facial proportions of sculptures on different monuments, and we found that most of the monuments at Mahabalipuram were executed not by Rajasimha but by earlier rulers. We are working on sculptural material from other parts of India as well. Application of computer methods in the analysis of sculpture remains an exciting field in India, and we are developing new methods to answer old questions.

Acknowledgment

We thank our colleague R. Chandrasekaran for his help in developing the software that we used.

References

1. G. Siromoney, M, Bagavandas, and S. Govindaraju, "An application of component analysis to the study of South Indian sculptures," Computers and the Humanities 14, No. 1, pages 29-37 (1980).
2. K. R. Srinivasan, Temples of South India, National Book Trust, New Delhi (1972).
3. T. A. Gopinatha Rao, Elements of Hindu Iconography, Volumes 1 and II (Second Edition), Indological Book House, Delhi (1971).
4. S. Govindaraju, Computer Analysis of Measurements of the Pallava Sculptures of South India, doctoral dissertation, University of Madras (1982).
5. G. Siromoney, "Mahabalipuram: costumes and jewellery," Madras Christian College Magazine 39, pages 76-83 (1970).
6. G. Siromoney, S. Govindaraju, and M. Bagavandas, "Iconometric study of Pallava Somaskandas," Kalakshetra Quarterly 5, No. 1, pages 31-38 (1982).
7. J. A. Hartigan, Clustering Algorithms, John Wiley & Sons, Inc., New York (1975).
8. M. Lockwood, G. Siromoney, and P. Dayanandan, Mahabalipuram Studies, Christian Literature Society, Madras (1974).
9. E. Guralnick, "The proportions of some archaic Greek sculptured figures: a computer analysis," Computers and the Humanities 10, No. 3, pages 153-169 (1976).
10. K. R. Srinivasan, The Dharmaraja Ratha and its Sculptures, Mahabalipuram, Abinav Publications, New Delhi (1975).
11. G. Siromoney, M. Bagavandas, and S. Govindaraju, "Iconometric analysis of the sculptures of the Dharmaraja Ratha," pages 137-150 in SRINIDHIH: Perspectives in Indian Archaeology, Art and Culture, Shri K. R. Srinivasan Festschrift, New Era Publications, Madras (1983).