What have you got there, Yunxiao Xiao?

March 3, 2022

In the series "What have you got there?" Princeton faculty and graduate students spill the beans on their research objects.

Yunxiao Xiao is a graduate student in the Department of East Asian Studies. In her dissertation "Scribes, Scholars, and Their Practices: The Making of Textual Knowledge in Early China,” she studies books, scholars, and the epistemological practices in early and medieval China. She is a specialist on early Chinese bamboo manuscripts and in this interview she introduces us to a mathematical table she has been working on, the Suanbiao 算表 manuscript


MARBAS: Can you tell us about the object that you are currently studying or have been wanting to study?

YX: Before the invention of paper, except for a few cases of texts that were written on silk, early Chinese texts were primarily written on bamboo or wood slips that were bound together. One bamboo manuscript that I have been working on is a mathematical table, the Suanbiao 算表 manuscript, which is now preserved at Tsinghua University. It consists of twenty-one bamboo slips, each about 1.2 cm wide by 43.5 cm long, and dated around 305 BCE. The manuscript was carefully arranged in a matrix structure: across the manuscript’s rectangular surface, the slips are horizontal and regularly spaced to create an even grid over the entire table. Each square in the grid is filled in with a number, creating a decimal multiplication table with the numbers distributed in a regular pattern. (Fig. 2)

Tsinghua University suanbiao Transcription
Fig. 2 Tsinghua daxue cang zhanguo zhujian vol.4, illustration 4.

The table is also paired with navigational threads next to the first column and first row that can direct the readers to the results of the calculation efficiently and accurately. (Fig. 3)

Tsinghua University suanbiao table numbers
Fig. 3 To calculate, an example would be 50 x 60=3000, or 50 x 2=100, etc.

How did you discover this object and what made it special that you took note of it? Were you excited to find it? If so, why?

In most cases, even when the bamboo or wooden slips were able to survive, their original binding threads made of hemp or silk that tied the manuscript together to form scrolls had long decayed. As such, our tasks of reconstruction are both textual and material: on one hand, we need to reconstruct the original sequence of slips in order to understand the texts; on the other hand, we also hope to recover the manuscript roll and retrieve the original form and format of early books.

In this regard, the Suanbiao MS is especially interesting both for its content and its unique “twice-folded” book format. Based on its tabular layout and clear numerical order, we now have a comparatively reliable reconstruction of the slips’ sequence. Furthermore, besides its writings, multiple vestiges of production, use, and preservation allow us to discover the book’s format and actual practices behind it.

Tsinghua University suanbiao imprints, threads
Fig. 4 Imprints of inks Fig. 5 Threads Fig. 6 Mirrored Smudges

For instance, there are several imprints of inks (Fig. 4) and threads (Fig. 5), and of mirrored smudges (Fig. 6) that still remain clearly visible to us.

Tsinghua University suanbiao diagram imprints
Fig. 7 Diagram

Especially the imprint of mirror images of characters from another slip or of binding threads betray that the corresponding slips were stored face-to-face for a long time (Fig. 7).

Tsinghua University suanbiao folded
Fig. 8 Diagram of the folded Suanbiao MS


Due to insufficient archaeological context, these mirrored traces are the very keys to understanding their spatial relations. On the basis of numerous imprints and mirrored traces, ultimately, I propose that the Suanbiao MS was not in scroll form with the bamboo slips rolled together, but in a unique book format that we have not seen before, in which the manuscript’s two sides were first separately folded, and then folded again toward the center. (Fig. 8, I rearranged the sequence of slip 1 and 2)

Can you tell us more about the way in which the object came about? Who was involved, where was it made, when, why? How was it used?

As is often the case of unprovenanced manuscripts, much precious archeological information has been lost forever. Scholars have dated this manuscript “middle to late Warring States,” or around 305 BCE, because of 1) the paleographic characteristics, 2) the results of radiocarbon dating of the bamboo, and 3) historical events that were recorded on the other manuscripts that presumably originated from the same tomb, which was more likely located in today’s Hubei or Hunan provinces, the area of the state Chu at that time. For another, we know very little about any person associated with the object—its producer, user, owner, or as its author or scribe, since there is no such information in the manuscript. However, although these people did not explicitly reveal their identities, we can still speculate about their working methods, the principles they followed, and the scribal or scholarly practices behind the written object. That is, in order to use the table, the manuscript had to be fully laid out to search the results of calculation through its visualized, tabular structure, with the help of the navigational threads. In this design, the tabular layout and the carefully deployed directional threads would navigate the reader to the desired answer with efficiency. Moreover, as the two margins of the manuscript were at the central part of the scroll, this special book format also indicates that the Suanbiao MS was a stand-alone codicological unit, it was not written with any other texts, and was not a chapter, nor a section, of a larger written project. Ultimately, all these paratextual, visual, and material dispositions were connected with its special method of use. That is, the Suanbiao MS was not made to be utilized in the normal epistemological practice in early China as “reading while unrolling,” but rather, as a display of a massive group of computational results, it was meant to be visually searched rather than sequentially read.

How does the object contribute to your research? How can it be used to understand the past?

My dissertation, “Scribes, Scholars, and Their Practices: The Making of Textual Knowledge in Early China,” explores the intricate interplay between material condition, mechanics, and human agency in early Chinese textual culture. Emphasizing the recently discovered bamboo, silk, and wooden manuscripts as contingent, context-bound material objects, I believe that their significance must be understood within their specific function, occasion, and context. The Suanbiao MS, as a starting point, affords us a glimpse into the diversity and complexity of the ancient books, readers, and their reading practices. “What was the correct sequence of bamboo slips?” and “What did the scroll look like?” are the most fundamental questions, and these questions concerning its materiality lead us to keep asking the deeper reasons that shaped the material forms and textual traditions. Thus, my dissertation also focuses on the idea that the significance of a discovered manuscript does not only lie in the ancient texts it conveys, but it also in its physical reality—and, most importantly, it stands for a moment, a condition, and a group of people.

How would you use it in your teaching?

I believe the Suanbiao MS would be a revealing teaching tool for many kinds of classes. The characters on the object are not as complicated as those of other manuscripts predating the Chinese empire: as a mathematical table, it is all about numbers, so even students taking first-year Chinese could fully engage with the manuscript as a type of authentic material. For a Chinese/East Asian history class, the manuscript directly demonstrates different possibilities of ancient Chinese book format, and the questions of materiality immediately bring up the discussions of the history of reading and learning. For a global or comparative history class, it could also be useful since the transformations of books, from scrolls to codex, from more cumbersome writing materials to paper, and even from manuscript culture to printing culture are issues that have intrigued book historians across time and traditions. I believe the comparison between materials of different traditions would spark some interesting discussions. Finally, as a mathematical manuscript, probably the earliest decimal multiplication table, reading this object together with the Babylonian mathematical table in a history of science class would also be instructive.

Further reading:

Tsinghua daxue chutu wenxian yanjiu yu baohu zhongxin 清華大學出土文獻研究與保護中心 [led by Li Xueqin 李學勤], eds. Tsinghua daxue cang zhanguo zhujian vol.4 清華大學藏戰國竹簡 (肆). Shanghai: Zhongxi shuju, 2013.

Yunxiao Xiao, “Restoring Bamboo Scroll: Observations on the Materiality of Waring States Bamboo Manuscripts,” Chinese Studies in History 50 (2017): 235–354.


Are you a Princeton faculty member or graduate student who would love to share your research object(s) with us, please contact Stephanie Luescher ([email protected]).