Dear old work platform, it's not you, it's us. Actually, it is you. And it was love at first onboarding. Their beautiful dashboards, their customizable workflows got us floated. Welcome to the New Books Network. What are numbers, and where do they come from? Based on her groundbreaking study of material devices used for counting in the ancient Near East, Karen Lee Overman proposes a novel answer to these timeless questions.
Tune in as we talk with Karen Lee Overman about her book, The Material Origin of Numbers. You're listening to New Books and History of Science, a channel of the New Books Network, and I'm your host, Michael Morales. Karen Lee Overman earned a doctorate in archaeology from the University of Oxford and is a research fellow at the University of Bergen, Norway. Lee, welcome to the show, and why don't we begin with having you tell us about yourself and your journey to writing about numbers.
When I retired from my first career in 2003, I went back to school. I took classes in anthropology and philosophy, and I was immediately hooked on both. I then finished a master's degree in psychology and a doctorate in archaeology. While this educational background might seem a bit eclectic, it's proven to be a nice starting point for the kind of research I do, since numbers have to be approached from multiple perspectives, particularly psychology, anthropology, and philosophy.
Brains, bodies, and material forms are put together with constructs from the philosophy of mind, which is the branch of philosophy concerned with the nature of human cognition and the role of material forms in it. Many theories about where numbers came from are philosophical in nature. but your contribution really comes from archaeology. How does archaeology help you think about the origin of numbers? Most theories about the origins of numbers see them as originating in the mind in some fashion.
2500 years ago, Plato said numbers were universals, invisible, eternal entities that we somehow come into contact with. Most of today's researchers in the cognitive sciences see numbers as brain-bound, either constructed mentally or emerging out of language. The problem with a purely mental explanation is that it cannot explain numerical variability across cultures.
While Western societies have lots of numbers, some traditional societies have very few, and the Pitaha of Amazonian Brazil are said to have no numbers at all. If numbers are mentally or linguistically constructed, why don't we all have them? After all, as members of the same species, we all share essentially the same brain and body, we all have language, and while our environments vary according to where we live on the planet, quantity is quantity wherever we go.
I think there is a simple answer. Numbers vary cross-culturally by whether we use material devices to represent them, which devices we use, and how we use them. But this answer takes us outside of a completely mental explanation. What I am doing in my research is looking at the material component of numbers. Not the things numbers are used to count, but the things used to represent numbers, like fingers, tallies, tokens, and numerical notations.
It isn't a stretch to think of material things as having a role in our conceptualization. As Colin Renfrew once observed, it would be inconceivable for us to have concepts of weight without the physical experience of weight. But with numbers, we have a conceptual system that starts with the perceptual experience of quantity.
From that perceptual starting point, we use things like fingers and tallies to make that experience tangible and manipulable. And in using and rearranging the devices, we get new ideas about what numbers are and how they work. So whereas others assumed the philosophical origin of numbers, the concept of numbers, which then led to material expression,
You suggest that it was the material devices used to count and calculate that led to the concept of numbers. Would you elaborate on how your research in archaeology led you to this conclusion? Humans have the ability to perceive quantity. We share this ability with other animal species. It's been found in so many other species to date that at this point it would be astounding if we found one without it. This perceptual ability lets us appreciate singles, pairs, and trios without counting.
Beyond three or four items, we see only many. While we cannot change the way this perceptual system works, we can use material forms to unpack what lies beyond the appreciable range of about three or four. For example, 5 and 10 are typically the first numbers to emerge from the undifferentiated many.
They are initially as many as the fingers on one or both hands. So, while we cannot directly appreciate these quantities, we can use material forms like the fingers to make them tangible and intelligible. A follow-on question might be, why is the hand a material form that an archaeologist would be concerned with? I would say first that it's interesting that congenitally blind people don't count on their fingers.
This shows there's no internal or mental capacity behind finger counting. Rather, the visual experience of the hand as a material object is what makes us use it for counting. The fact that the hand hasn't been considered previously for its material properties has been a significant problem in understanding numerical origin. Historically, the hand has been considered biological and ignored, or more recently embodied and contributing to processes that are purely mental in nature.
Similarly, written numbers have been considered symbolic and mental rather than material. Only physical devices like tallies and abacuses have been considered as falling within archaeology scope, and even here there is a shortfall because it ignores the ephemeral forms created by sorting behaviors.
Because fingers, symbols, and physical devices have been considered ontologically distinct, the sequence of material forms that takes us from the perceptual experience of quantity to symbolic numbers has been disconnected in a fatal way.
On the other hand, once they are all put together on the basis of their role in representing numbers as material forms, we have a naturalistic way of explaining how symbolic numbers can emerge from the perceptual experience of quantity that we share with other species. Your work is in line with what is called Material Engagement Theory, M-E-T. Would you explain this theory for us?
Material engagement theory is the idea that material forms have a role in cognition. It's a framework for archaeological analysis that borrows concepts from the philosophy of mind. The archaeological record shows us that we have been using tools for at least three and a half million years. Historically, the thinking has been that the archaeological record is simply a witness to the increasing powers of the human mind, the idea that bigger brains make better tools.
But that's only half the equation. Material engagement theory looks at the other half, the idea that using tools changes behaviors in brains. Learning to read is a good example of this. Literacy means that someone has acquired a suite of specific changes to brain processes like object recognition and lexical recall and behavioral abilities like hand-eye coordination and fine motor control.
But seeing literacy and reading like this also means that we have to think of writing as a material form. And that is what lets us analyze things like writing and numbers with material engagement theory. So, Lee, what else are you working on these days? I'm currently publishing a book on cultural number systems because I'm just amazed at how different numbers can be in different times and places and how impressively clever we are as a species.
I've also just finished some articles on how numerals work as a material technology for numbers. I'm currently applying my insights into numbers and writing to the origin and nature of symbols more generally. And I finally got a solid outline for my next book, which will be about how literacy emerged from early writing systems. How is your work relevant for the study of the ancient Near East?
My work is relevant to the study of the ancient Near East because Mesopotamia has perhaps the most important number system in all of history. Its numbers are the earliest that are unambiguous to modern eyes. Its archaeological and textual records show a clear chronology in the technologies used for numbers, fingers, tallies, tokens, and written notations. This insight is critical to understanding how numbers emerge and become elaborated cross-culturally.
I also worked with Denise Schmant-Besserat to expand her token database with over 2,300 new entries, analysis that I present in my book with Gorgias Press. Lee, we're grateful for your sharing your expertise on the interesting topic of numbers. And friends, we thank you for listening to this show on the History of Science, a channel of the NewBooks Network. Until next time, goodbye.