Humans have been drawing lines and circles to grasp geometrical concepts and describe the laws of nature for about 5,000 years. But most scholars have approached the history of ancient mathematical sciences through close examinations of texts and writings, an area of study called philology.
Eunsoo Lee, a PhD student in classics, hopes to expand that scholarship by tracing the changes and variations in diagrams over the course of human history.
"Diagrams can tell us a lot about visual norms of the day," Lee said. "Languages we speak affect how we think, but the visual images we draw also shape our thought."
Over the past six years, Lee has examined changes in diagrams used in Elements, a collection of 13 books on mathematical and geometric concepts attributed to Euclid, the ancient Greek mathematician who lived in Alexandria, Egypt, around 300 BCE. He is attempting to build a database of diagrams as part of his dissertation project.
From mathematics to classics
According to historians and scholars, Elements was deemed to be the most popular pre-20th-century textbook. The work, written about 2,300 years ago, was the second-most printed book after the Bible at one time.
Lee first read Elements during his undergraduate years at Seoul National University, where he earned a bachelor's degree in mathematics.
"I was fascinated by its simple logic and structure," said Lee, a 2016-17 Geballe Dissertation Prize Fellow at the Stanford Humanities Center. The work inspired Lee to pursue the study of classics and examine the work of other ancient scientists.
Historians and classists have studied in detail the language of Elements -- which was first written on papyrus in Greek - and how its text changed over time. But the work's diagrams, essential to its geometrical concepts, were left out of those studies.
"Until recently, no one has really examined the visual side of ancient science," said Reviel Netz, professor of classics and Lee's adviser. "You would try to recover the words that people said but you didn't try to recover the visual impact, the images."
Lee was puzzled by what he calls "a blind spot" in the study of Elements and similar ancient works, some of which changed drastically over the centuries after numerous copies and translations. Lee said this puzzlement was the seed for his dissertation project at Stanford.
Netz called Lee's attempt to reconstruct and study the visual history of Elements unique and groundbreaking for the field of classics.
Recent scholarship has shown that diagrams are an essential part of demonstrating the scientific meaning of an argument, Netz said.
"We've come to realize just how central images are to scientific thinking," Netz said. "You do one kind of science when you assume that diagrams are precise pictures, and you do a different kind of science when diagrams are assumed to be just rough sketches."
"The changes in the diagrams reflect the culture and custom of that particular age and time," Lee said. "By examining them, we also get a better understanding of how visual knowledge has been created and transmitted."
In the course of his project, Lee has traveled numerous times to Europe to study more than 175 copies of Elements - from the earliest known Greek manuscript from the 9th century to the early printed editions in the 15th and 16th centuries.
As Elements was reproduced over hundreds of centuries, the work was adapted for new audiences. Examining the transmission and translation of diagrams over such a long time became a vast, challenging game for Lee.
In some cases, manuscript makers introduced errors into the diagrams that carried over to future copies. In other cases, the diagrams were meticulously transmitted and enhanced to better explain geometrical concepts to a different audience. For example, as the work's distribution increased and parchment codex replaced papyrus rolls, what was earlier presented as one complex diagram was divided into two or more simpler drawings.
"The diagrams were not merely copied and reproduced, but transmitted and transformed, reflecting the fashion and norms of each age," Lee said.
When the work was translated into Latin and Arabic from Greek, more changes were introduced. In the Arabic copies, the diagrams' orientations and letters were switched to accommodate a right-to-left reading audience.
But Lee also found that some Greek manuscripts carried the same switched diagrams. Lee said this finding is one of the most interesting discoveries he has made, because classics scholars overwhelmingly believe that Greek manuscripts precede the Arabic ones.
"I believe this suggests we have to open the possibility that some Arabic diagrams might have influenced the early Greek diagrams," Lee said.
The printing revolution in the 15th century marked a significant footprint in the history of diagrams, Lee said. The makers of the diagrams, who were previously largely unknown, became recognized as authors. The diagrams themselves became exposed to competition, he said.
"The competition naturally resulted in diagrammatic criticism and led to the invention of more practical drawing of diagrams to attract more readers," Lee said.
A 'lifelong' project
Aside from tracing the changes in diagrams themselves, Lee is also trying to develop a framework for how to distinguish them and record their differences.
"The methodology for examining diagrams remains in its infancy," Lee said. "And there is no consensus regarding how it might address the reconstruction, comparison and tracing of diagrams, which therefore are neither acknowledged nor investigated in any significant depth."
Lee hopes to continue to trace the history of visual knowledge and expand his analysis beyond Elements. But he recognizes that the task is of enormous proportions, particularly because of the need to examine a large number of ancient texts, most of which remain scattered across libraries in different countries and are available for limited viewing.
"It's a huge project," Lee said. "It's a lifelong plan."