QUANTA researchers publish theme issue in the world’s oldest scientific journal

In 1951, the Ministry of Church and Education introduced a new way of counting in Norwegian schools and state administration offices. Before this counting reform, it was common to say the units before the decades when reading numbers above 20 out loud (en-og-førti, for example), as in German. But the new way of reading numbers put the decades before the units (for example, førti-en), as in English. At the time, many thought the proposed reform offered a more 'logical' or 'natural' way of counting, especially given the then-new six-digit phone numbers and the confusion that sometimes occurred when reading these out loud. After all, we read Indo-Arabic numerals (41) from left to right, and so we read the decades before the units, so why would we say them in the opposite order?

Scaling up: How the way we count shapes the way we think

This episode of Norwegian history illustrates well the importance of recent research on the base of numeration systems, published by a team from the Department of Psychosocial Science at the University of Bergen in a theme issue of the world's oldest academic journal, the Philosophical Transactions of the Royal Society. UiB researchers Andrea Bender (UiB) and Jean-Charles Pelland (UiB) have edited the latest special theme issue together with Mary Walworth (CNRS) and Simon J. Greenhill (University of Auckland).  

The Norwegian counting reform shows that we learn to master many different ways of representing numbers, and that some of these work better with numeral systems governed by similar compositional rules. While these systems typically rely on having a base — a number whose powers receive special representational status within the system — not all systems have the same base, and even systems with the same numerical base can be structured differently. These base interactions can affect how easily we learn systems, and can determine which types of systems will tend to be used in which contexts, raising questions about what causes these cognitive effects.

The cognitive and cultural implications of the base of a numeration system

In their work the UiB researchers, Andrea Bender (professor), Jean-Charles Pelland (postdoc), Olga Dudojč (Phd) and Chiara Anceschi (PhD), four members of the ERC Synergy Grant project QUANTA, explore the cognitive and cultural implications of the base of a numeration system, breaking new ground on an important aspect of our cognitive lives.

Bender's article studies such interactions between bases at both the cognitive and cultural levels. There are many well-known cases of interactions between bases, not all of which were good. The Swedish battleship Vasa, for example, capsized in 1628, owing to discrepant measurements of feet, costing many their lives. On the cognitive side, the fact that Norwegians used counting practices that had inverted orderings in parallel for decades after the reform shows that having different structures to the base systems we master can influence how well we adapt to new systems. Beyond effects like those targeted by the Norwegian counting reform, Bender's previous work shows that parallel use of systems and the associated base interactions – some of which have positive consequences, others not – are the product of cultural evolution, where the mind shapes culture, and vice versa. 

To make progress on such work, terminological consistency among disciplines is key, given that we often master systems in different modalities like notations and languages. Unfortunately, as Pelland argues in his contribution to the theme issue, the way bases are framed varies tremendously between linguistics and the study of notation. To help get everyone on the same page, Pelland's contributions offer a novel terminological framework around the concept of compositional anchors, of which bases are a special case.

Finally, getting back to earth, the work done by Dudojč and Chiara Anceschi studies how numeration systems are implemented in the body. Presenting the first comprehensive analysis and categorization of body-based numeration systems around the world, Dudojč and colleagues offer us a bird's eye view of the compositional landscape in a representational format that we use almost on a daily basis, and yet that we know very little about. 

These are just three of the 17 articles that are now available open access on the journal's website, each of them using the concept of a base to further our understanding of how an interplay between our minds and our cultures led to the rise of our numerical abilities. The story of the Norwegian counting reform shows that we have been dealing with bases and their cognitive implications for a long time. Now, for the first time ever, we have a targeted study of these implications. While this work may not lead to similar reforms, it has the potential to transform how we think about an important yet overlooked cognitive tool.