Evidence of Mathematical Sciences and Technology in the Seokguram Grotto

One of the secrets which allowed for the preservation of the grotto is the ventilation system that the Silla builders used to combat the normal humidity that would have occurred otherwise inside the man-made cave. They took advantage of a natural feature in the mountain itself, a spring, by digging out the grotto above it so that any occurring condensation would settle low on the floor rather than around the walls of the grotto itself, therefore preventing weathering and decay. However, there has naturally been wear and tear and accelerated damage due to acid rain and pollution as well as from earlier clumsy restoration efforts in the early 1900s which caused extensive damage that is now only becoming more and more apparent.

Just as we saw in Bulguksa Temple and Cheomseongdae, the artists who worked on the grotto and the Buddha statue implemented mathematical ratios that had significance in Buddhism. For instance, the statue was built using the Buddhist equivalent to the golden ratio. When measuring the proportion of the statue’s face, chest, shoulders, and knees, the statue faithfully follows the Buddhist ideal measurement of beauty and harmony — 1:2:3:4. Other mathematical ‘tweaks’ shall we say, were used by the artists to trick the viewers into seeing something that wasn’t actually true. For instance, the halo that encircles the statue’s head, when looked head-on from the hallway leading to the grotto, looks perfectly circular. It is only when one stands directly beneath the statue and looks up that we can see that the halo is in fact an elliptical shape. This was necessary when the artist took into account that the statue which stands at 3.5 meters would be seated atop a lotus flower podium which is 1.34 meters and viewed by visitors from the entrance of the hallway which is a distance of 10 meters. From that angle and distance, the ellipse halo, therefore, looks circular. Another example of the artists tweaking measurements to deceive the naked eye is seen in the hands of the Buddha. In the classic mudra position, the right-hand points downward and the left hand is horizontal. It is only evident when viewed at a close distance that the left hand is actually larger than the right. This is because when the statue is viewed from the perspective of a viewer looking up and from about 10 meters away, the hands would have looked markedly different in size. By making the left hand bigger, the naked eye is tricked into thinking that the two hands are the same size. The head of the statue is also a lot bigger and would not be anatomically possible in real life. Again, this is to ensure a proportional balance to a viewer from the proper distance and perspective.This tweaking by artists and architects was not unheard of in the past. For instance, Leonardo DaVinci had to tweak his statue of David to fit the logistics of gravity and perception as well. His statue of David for example also had exceptionally large hands to evenly distribute the weight of the statue as well as correct the perception of viewers who would have been looking up at the statue as it stood high above.

This technique unknown to the Silla artists is now called perspective geometry. It was developed in Europe in the 18th century though we have seen uses in Europe as early as the 1500s (David was finished between 1501–1504). There have been much earlier examples in the temple of Karnak in Egypt where the towering statues were also carved with larger heads and smaller feet to adjust to the angle they were being seen. As I delve deeper into these lectures, I am truly amazed by how resourceful and ingenious the Silla artists and builders were. Even without realizing the mathematical fundamentals of geometry, they were able to identify a problem and apply a practical solution that has its roots in science and mathematics.