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Intellectual history

What the Digital Dark Age Can Teach Us About Ancient Technologies of Writing

Editors’ Note: due to the disruption of academic networks and institutions caused by the ongoing Coronavirus pandemic, JHIBlog will shift to once-a-week publication for the time being, supplemented by a selection of older posts from our archives. We are grateful for our readers’ understanding, and hope to resume normal scheduling as soon as possible.

By guest contributors Sara Mohr and Edward C. Williams

In contemporary science fiction it is hard to avoid the trope of an archaeologist or explorer unearthing a piece of ancient advanced technology and finding that it still functions. This theme may have its roots in the way we often encounter artifacts from the ancient world—decayed but functional or legible, as material culture and/or as carriers of written language. However, the prototypical “ancient technology” in fiction often resembles the electronic information technology of our modern age. Keeping our modern technology active and functional requires orders of magnitude more energy than the neglect implied by ancient ruins—delivery of spare parts fueled by cheap energy, complex schematics and repair manuals, and even remote connections to far-off servers. The idea that our technology would work hundreds of years in our future without significant intervention is unbelievable. In a certain sense, a Mesopotamian clay tablet is far more similar to the ancient advanced technology found in media—if it’s in good enough condition, you can pick it up and use it thousands of years later.

Will the archaeologists of the future see the information storage of the digital age not as sources of knowledge about our time, but undecipherable black boxes?  The general problem of data preservation is twofold: the first is preservation itself and the second is the comprehensibility of the data. The BBC Domesday Project recorded a survey of British life in the 20th century on adapted LaserDiscs—a format that, ironically, requires considerable emulation (the process of enabling a computer to use material intended for another kind of computer) efforts to reproduce on a modern machine only 35 years later. This kind of information loss is often referred to as the coming of the Digital Dark Age (Bollacker, “Avoiding a Digital Dark Age”). Faced with the imposing pressure of a potential Digital Dark Age and the problematic history of modern data storage technology, perhaps it is time to rethink our understanding of ancient technology and the cultures of the past who were able to make their data last long into the future.

Scholars of the Ancient Near East are intimately familiar with the loss and recovery of written information. Our sources, written in the wedge-shaped script called cuneiform, are numerous and frequently legible despite being thousands of years old. Once the scribal practice that transmitted the script was interrupted, considerable scholarly work was required to reconstruct it, but the fundamental media of data storage—the clay tablets—were robust. Even then, many valuable tablets have been lost due to mishandling or improper storage. Despite the durability of the medium, once the system of replicating, handling, understanding, and deliberately preserving these tablets were lost much information was lost as well.

But cuneiform writing is more than just the act of impressing words onto clay with a reed stylus; it is deeply rooted in the actions and culture of specific groups of people. This notion is certainly true of technology as a whole. An interrelationship exists between all elements of a society, and each constituent element cannot be considered or evaluated without the context of the whole (Bertalanffy, General Systems Theory: Foundations, Development, Applications, 4). Rather than focus on the clay and the reeds, it is necessary to take into account the entire “socio-technical system” that governs the interaction of people and technology (Schäfer, Bastard Culture! How User Participation Transforms Cultural Production, 18). Comparative studies of cuneiform writing and digital technology as socio-technical systems can inspire further insight into understanding ancient technology and illuminating why it is that humble cuneiform writing on clay tablets was such a successful method of projecting information into the future, as well as informing us about the possible future of our contemporary data storage.

Only recently have those who work regularly with cuneiform tablets studied the technology of cuneiform.  Cuneiform styli could be made of various materials: reed, bone, bronze, or even precious metals (Cammarosano, “The Cuneiform Stylus,” 62). Reed styli were the most common for their advantageous glossy, waterproof outer skin that prevented them from absorbing humidity and sticking to the clay. Another key part of scribal training was learning the art of forming tablets by levigating and kneading raw clay (Taylor and Cartwright, “The Making and Re-Making of Clay Tablets,” 298), then joining lumps of clay together in a grid pattern or by wrapping an outer sheet of clay around a core of a thin piece of folded clay (Taylor, “Tablets as Artefacts, Scribes as Artisans,” 11).

But cuneiform technology goes beyond the stylus and tablet and must include the transmission of cuneiform literacy itself. Hundreds of thousands of legible cuneiform tablets have been found and documented to date, with many more in the processes of being excavated. With such perishable materials as clay tablets and organic styli, how is it possible that these texts have survived for thousands of years? Surprisingly, the answer may lie in how we think about modern technology, data preservation, and our fears of losing records to the Digital Dark Age.

The problem is growing worse, with more recent media demonstrating shorter lifespans compared to older media. We see a variety of different projects that look back to older forms of information storage as a stop-gap between now and the possibility of a Digital Dark Age. For example, The Rosetta Project, from the Long Now Foundation, has been collecting examples of various languages to store on a 3-inch diameter nickel disc through microscopic etching. With minimal care (and the survival of microscopy), it could last and be legible for thousands of years.

We tend to think that a return to older forms of information storage will solve the problem of the Digital Dark Age—after all, the ancient technology of stylus + clay preserved Mesopotamian data neatly into the modern era. However, such thinking results from an incomplete understanding of the function of technology as it applies to the past. Technology is more than just machinery; it is a human activity involving technological aspects as well as cultural aspects interwoven and shaping one another (Stahl, “Venerating the Black Box: Magic in Media Discourse on Technology,” 236). Regardless of the medium or time period, the data life cycle largely stays the same. First, people generate data, which is then collected and processed. Following processing comes storage and possibly analysis.

But in the end, we always have humans (Wing, “The Data Life Cycle”).

Humans are the key to why information written in cuneiform on clay survived as long as it did.  In ancient Mesopotamia, scribal culture meant copying the contents of clay tablets repeatedly for both practice and preservation. There are texts we know from only one copy, yet in order for that copy to survive several other copies had to have existed. The clay and the stylus did not ensure the preservation of cuneiform information—it was the people and their scribal practice.

It is somewhat surprising that the discussion of ancient technology has not yet embraced the social aspect that accompanies the machinery, especially when we so readily acknowledge its impact on modern technology. To avoid losing electronic data, users are exhorted to intercede and make regular backup copies. We also find that the history of obsolete technology is based in innovative technology that died as a result of socioeconomic pressures (Parikka, “Inventing Pasts and Futures: Speculative Design and Media Archaeology,” 227). The technology was perfectly sound, but it was never a good match to the social and economic times of its release.

This need for protection from loss largely comes from the idea that “electronic writing does not have the permanence of a clay tablet” (Gnanadesikan, The Writing Revolution: Cuneiform to the Internet, 268). However, those of us who work with clay tablets are more than aware of the frightening impermanence of the medium. We are well acquainted with the experience of opening a box meant to contain a cuneiform object only to find that it has been reduced to a bag of dust. It has been said that more redundancy usually means less efficiency, but that does not hold for all circumstances. Mesopotamian scholars generated redundancy through productive training, and we now look to redundancy to save our digital future. However, redundancy was not a part of the physical technology, but rather the surrounding cultures that used it.

At its core, writing is an information technology. It is a system of communication developed for use by particular groups of people. In the case of cuneiform, the scribe who wrote the latest known datable cuneiform tablet composed an astronomical text in 75 AD (Geller, “The Last Wedge,” 45). Despite being able to date its final use, the last wedge, we are still able to read and understand Akkadian cuneiform today. However, it was not the process of incising the wedge itself that made this continuity possible. Rather, it was the scribal culture of ancient Mesopotamia that committed to copying and re-copying over the course of millennia.

The possibility of a Digital Dark Age has the world thinking of ways in which we can adjust our cultural practice around technology. Examples from Mesopotamia highlight the importance of the connection between human activity and machinery in technology. We would do well as historians to take notice of this trend and use it as an inspiration for expanding how we study ancient technology like cuneiform writing to incorporate more on human attitudes alongside the clay and the reeds.

Sara Mohr is a PhD student in Assyriology at Brown University. Her research spans from digital methods of studying the ancient world to the social function of secrecy and hidden writing. 

Edward Williams (Brown ‘17.5) is a software engineer at Qulab, Inc, working on machine learning and computational chemistry software for drug discovery. He acts as a technical consultant for the DeepScribe project at the OI, developing machine learning pipelines for automated cuneiform transcription.

Categories
Intellectual history

Genres of Math: Arithmetic, Algebra, and Algorithms in Ancient Egyptian Mathematics

By contributing author E.L. Meszaros

As non-native readers of Egyptian hieratic and hieroglyphics, our understanding of the mathematics recorded in these languages must necessarily go through a process of translation. Such translation is both necessary to allow us to study these problems, but also precarious. If done improperly, it can prevent us from true understanding. One way that we approach translating Egyptian math problems is by grouping them into genres, using categorization to aid in our translation by thinking about problems as algebraic or geometric equations, crafting them into algorithms, or piecing together word problems from their prose. If the process of understanding Egyptian math problems relies so heavily on translation, and translation in turn is influenced by categorization, then we must consider how our processes of categorization impact our understanding of ancient Egyptian math. 

The necessity of translation for the modern study of ancient mathematics has been the source of a great schism within the community. In an infamous 1975 paper, Unguru argued that one of the unintentional consequences of translation was the attribution of algebraic thinking to these ancient cultures. Mathematicians and historians tend to translate the word problems of ancient Iraq or Egypt into the abstracted symbolic statements we are familiar with today. This has helped us to better understand ancient mathematical ideas, but has also done a disservice to the math itself. The process of abstraction manipulated the geometry or arithmetic of ancient math into algebra, a way of examining mathematical problems that Unguru argued these ancient cultures never used (78).

Image of a fragment of the Moscow Papyrus showing problem 14 on how to calculate the volume of a frustum. The top portion shows the original hieratic, which has been translated below into Egyptian hieroglyphics.

However, others have pushed back against Unguru. Van der Waerden suggests that Unguru has misunderstood “algebra” by attributing such importance to the symbolic representation of data. Rather, van der Waerden emphasizes the convenience of symbols as a way of interpreting, analyzing, and comparing data, rather than the structural language of understanding data (205). Freudenthal similarly takes umbrage with Unguru’s understanding of what algebra is. “Symbols,” he writes, “…are not the objects of mathematics…but rather they are part of the language by which mathematical objects are represented” (192).

We can compare the strict translation of an Egyptian word problem to its algebraic translation by looking at problem 14 of the Moscow Papyrus.

Prose English translation:
Method of calculating a / ̄\.
If you are told a / ̄\ of 6 as height, of 4 as lower side, and of 2 as upper side.
You shall square these 4. 16 shall result.
You shall double 4. 8 shall result.
You shall square these 2. 4 shall result.
You shall add the 16 and the 8 and the 4. 28 shall result. 
You shall calculate  ̅3 of 6. 2 shall result.
You shall calculate 28 times 2. 56 shall result.
Look, belonging to it is 56. What has been found by you is correct. (Translation by Imhausen 33)

Algebraic Translation:
V = 6 (22 + (2*4) + 42)/3

Abstracted Algebraic Translation:
V = h (a2 + ab + b2)/3
where
h (height) = 6
a (base a) = 2
b (base b) = 4
V = volume

The algebraic translations are at once easier to take in but also visibly shorter, clearly missing information that the prose translation contains.

As an alternative to these translation techniques, Imhausen proposes the use of algorithms. Imhausen suggests that we translate Egyptian mathematical problems into a “defined sequence of steps” that contain only one individual instruction (of the type “add,” “subtract,” etc.) (149). These algorithms can still represent math problems in multiple ways. A numerical algorithm preserves the individual values used within Egyptian problems, while a symbolic form abstracts the actual numbers into placeholders (152). 

Numeric Algorithmic Translation:
6
4
2

  1. 42 = 16
  2. 4 x 2 = 8
  3. 22 = 4
  4. 16 + 8 + 4 = 28
  5.  ̅3 x 6 = 2
  6. 2 x 28 = 56

Here the first three numerical values are the given bases and height from the problem. The unfamiliar ” ̅3″ is the standard way of writing a fraction of 3, namely 1/3, in ancient Egyptian math.

Symbolic Algorithmic Translation:
D1
D2
D3

  1. D22
  2. D2 x D3
  3. D32
  4. (1) + (2) + (3)
  5.  ̅3 x D1
  6. (5) x (4)

Drawing out the scaffolding of the problem by defining such algorithms allows scholars to easily compare math problems. The abstraction into symbols, the removal of extraneous information, and the sequential rendering allow us to more easily notice variation or similarity between problems (“Algorithmic Structure” 153). Imhausen suggests that identifying the substructure encoded beneath the language of presentation allows us to compare individual math problems not only with each other, to generate groups of mechanisms for solving and systems of similar problems, but also to look cross-culturally. Breaking down problems from Mesopotamia, China, and India may reveal similarities in their underlying algorithmic structures (158). 

The generation of algorithmic sequences from Egyptian word-based math problems does not solve all of our translation problems, however. Any act of translation, no matter how close it remains to the original language, is a choice that necessitates forgoing certain options. It also allows for the insertion of biases on the part of the translator themselves—or rather, such insertion is unavoidable.

In the example from the Moscow Papyrus, for example, the initial given values of the frustum are not specifically identified. The images from the original problem are missing, as are the verbs for the mathematical operations. Imhausen herself points out that this algorithmic form reduces some interesting features. The verb “double” in the original problem, for example, is replaced with “x 2” in the algorithmic translation (75). Making these changes requires us to confront the choice between algorithmic structure and staying true to the source material. “Fixing” these differences allows us to more easily compare math problems, but also presumes that we know what was intended.

The translation of Egyptian math problems into schematic algorithmic sequences is, therefore, not without its own set of problems. While Imhausen claims that they avoid some of the pitfalls of translation into algebraic equations that have so divided the community (158), algorithm interpretations are still likely to present the material in a way that differs from how ancient mathematicians thought about their own material. However, when applied carefully, such mapping may provide valid interpretations of these texts and a focal point for comparison.

Thinking about the genre of translation, the use of algebraic or geometric or algorithmic tools to interpret ancient math, is important for a number of reasons. We have already seen that the choice of genre impacts ease of understanding. Modern scholars used to thinking about math problems in an algebraic format will, unsurprisingly, read algebraic translations more easily. But these choices also impact what aspects of the original we preserve — algebraic translations lose information about the order of operations and remove the language used to present the problem.

However, paying attention to generic classification can also prevent us from reading ancient math problems with the “Western” lens. While algebraic interpretations are an artifact of modern scholarship, they are also an artifact of European scholarship. Too often the idea of geometry is put forward as an entirely Greek invention, while algebra is thought of as belonging to Renaissance Europe. By privileging these ways of thinking about ancient math problems we may be inherently white-washing native Egyptian thinking. Prioritizing algebraic interpretations, even if they aid in understanding, work to translate Egyptian math into the more familiar “Western” vernacular. Instead, scholars should work with the unfamiliar and think about these math problems without filtering them through these modern concepts.

Regardless of who one sides with in the debate between algebra and arithmetic, prose and algorithm, we must be cognizant of the fact that categorizing ancient Egyptian math is a conscious choice that influences how these problems are understood. Much like the act of translation itself, categorization is a process that is inherently influenced by the biases—intentional or otherwise—of the scholar. There may be nothing wrong with thinking about Moscow 14 in terms of an algebraic equation as long as we understand that this is an act of translation from the original and, therefore, reflects a reduced understanding of the native problem itself and incorporates aspects of the translator’s biases.

Which is all to say: tread carefully, because even numbers are not immune to the bias of translation.

E.L. Meszaros is a PhD student in the History of the Exact Sciences in Antiquity at Brown University. Her research focuses on the language used to talk about science, particularly as this language is transmitted between cultures and across time.