Philosophical Transactions B recently published a theme issue on ‘A solid base for scaling up: the structure of numeration systems’. In this blog, Guest Editors Andrea Bender, Jean-Charles Pelland, Simon Greenhill and Mary Walworth tell us how this issue came about, and about some of the important research highlighted in this issue.
Like many scientific discoveries, this theme issue is the happy result of things not quite going as planned. Our plan was for anthropologists, linguists, philosophers, and psychologists to share data on numeration practices from their respective fields, with the aim of categorizing them and finding patterns among the categorized data. To carry out this plan, a workshop was organized by members of the QUANTA project, an initiative whose main aim is to uncover the evolutionary roots and trajectories of numeration practices around the globe, thanks to funding by the European Research Council with a synergy grant.
Unfortunately, once the meeting got underway, it quickly became apparent that researchers were using the same words to mean different things. Some numeration systems were labelled as being quinary by some, decimal or vigesimal by others - while some argued it was all three options at once! Owing to this terminological confusion, instead of looking for patterns among the categorized data, people were disagreeing about how to categorize the data in the first place. Things were clearly not going as planned. History teaches us that confusion around numeration systems can have profound implications, as exemplified by the costly crash of the Mars Climate Orbiter in 1999, which was the result of conflicting measurement units. Similarly (though with less serious implications), the confusion encountered at the QUANTA meeting was due to conflicting conceptions of a key cultural tool that scaffolds numerical cognition: the base of a numeration system.
To get back on track, we needed a unifying conceptual scheme that captures what bases are across languages, notations, and other representations of numbers. After long discussions and even longer email chains, such a conceptual scheme was eventually codified in the Glossary that accompanies this theme issue, which was then sent out to all authors at early stages of the writing process. With this novel terminological framework at their disposal, contributors to our theme issue break new ground with innovative research that shows how important the overlooked concept of a base – and the larger family of compositional anchors of which bases are special cases – really is for the study of numerical cognition. For example, Holt & Barner's article introduces new research methods that rely on use of non-decimal compositional anchors to see whether systems with smaller anchors can make it easier for children to learn what numbers are. Applying our framework to lesser-known systems, Dudojč and colleagues analyse data extracted from the first ever comprehensive database of body-based numeration systems, categorizing these in terms of the frequency and types of anchors they display. While some articles offer new ways of conceptualizing and categorizing bases, a few offer detailed analyses of cognitive and cultural implications of bases and their interactions, while others explore possible roots of compositional numerical abilities in languages from lesser-known cultures from Amazonia to Australia. Together, these articles show that focusing on the concept of a base can yield novel insight in fields such as developmental psychology and cognitive anthropology, the history of mathematics, and linguistics.
For centuries now, countless attempts have been undertaken to uncover when, how, and why our ancestors invented such widely different ways to represent numbers. And yet, we are only just beginning to understand their cognitive origins and evolutionary pathways. Unfortunately, because numeration systems straddle a wide range of domains across and beyond the life sciences, investigating their origins isn’t a sure-fire success. Miscommunication and terminological tangles between disciplines challenge such endeavours, which is why progress requires incentives for large-scale collaboration and a highly visible platform for communicating conceptual agreement across disciplines. For achieving the latter, putting together these articles for a theme issue of Philosophical Transactions was the natural choice.
Being able to publish in the oldest scientific journal in the world is the ultimate honour – primarily because of the distinctiveness and scientific excellence of the journal, but also because it has been a witness to, and itself is an example of, the very phenomenon we are interested in: cultural evolution. The format and history of the journal, which is celebrating its 360th anniversary, is meaningful for each of us:
Andrea Bender: As executive editor of Topics in Cognitive Science, a journal devoted to special issues, I burn for this format. Clusters of thematically related papers strike me as the culmination of scientific publishing because they allow for complex subjects to be illuminated from widely diverse perspectives and, ideally, in an interactive manner – a plurality of voices all communicating about a joint topic.
Simon Greenhill: Over my career, I've read many Philosophical Transactions special issues. I pay close attention to them as they are always a powerful tool for highlighting the state of play in a particular area and tend to reveal exciting new research pathways ready to explore.
Jean Charles Pelland: Editing papers for the same journal that published work by Sir Isaac Newton made it difficult to ignore his legacy, but it also reminded me of how messy scientific progress has always been, even for giants of history. Concepts, words, and notations spread through populations like organisms conquering new lands. This applies to forbidden dances like the lambada, but also to forbidden scientific notations like Leibniz’ calculus notation and, as I found out co-editing our special issue, to concepts like the base of a numeration system.
Mary Walworth: As someone devoted to interdisciplinary approaches to answering the big questions about human history, I’m thrilled to bring together research from multiple disciplines on a controversial yet important topic about our evolution. It is rare to have interdisciplinary insights on a subject in one place, and even rarer to be able to interweave those insights for a broader audience. In this way, our special issue on bases has given us an opportunity to present something relevant for multiple sciences, in a unique format accessible to so many.
In short, for us, guest-editing for Philosophical Transactions was educational and fun, as it gave us a chance to bring together new ideas from many disciplines on a topic that has been criminally under-studied. For our topic, it was both a blessing and a unique opportunity. Having the privilege of collaborating with a journal that cares not just about high-quality papers, but also about the themes they cover, has been a highly enriching and rewarding experience.
Read the theme issue ‘A solid base for scaling up: the structure of numeration systems’.
Visit our website to read more content from Philosophical Transactions B, or to find out how you can become a Guest Editor for the journal.
Image credits
Using a vintage wood abacus. Credit: bernie_photo/iStock.
Author photos provided by the authors.
