The story of numerals

Many Minds

Greetings, all! It’s been a minute, but we’re back, we’re refreshed, and we’re buzzing with excitement about the next few months of Many Minds.

This episode we’re talking about one of humanity’s most powerful cognitive tools: numerals. Numerals are those unassuming symbols we use whenever we read clocks, check calendars, dial phone numbers, or do arithmetic. My guest on today’s show is Stephen Chrisomalis. Steve is an Associate Professor of Anthropology at Wayne State University in Michigan, where he specializes in the anthropology of numbers, mathematics, and literacy. He’s the author of the recent book Reckonings: Numerals, Cognition, and History, which is the focus of our conversation today.

Humans have developed more than a hundred different systems for representing numbers over the last 5000 years or so. Steve and I discuss how these systems differ from each other. We talk about how they build on the ancient tally systems used in the Upper Paleolithic and how the develop hand-in-hand with writing. We consider the popular idea that the Roman numerals fell from favor because they’re no for good calculation. (Not so much, says Steve.) We also talk about some lesser-known numerical notation systems. Like the one the Cherokee polymath Sequoyah developed alongside his much-celebrated syllabary. And, of course, we cast a glance to the future. What kinds of systems might humans be using centuries or even millennia from now?

Numerals are—in and of themselves—pretty cool. But they become all the more so when we see them in broader context. As Steve’s book makes clear, numerals offer a compelling case study in how of our cognitive technologies are shaped by the vagaries of history, the dynamics of culture, and, of course, the constraints of the human mind.

Learned a lot from this one, folks—I think you’ll enjoy it. Without further ado, here’s my chat with Steve Chrisomalis.

A transcript of this episode is now available here.

Notes and links

3:20 – Dr. Chrisomalis’s doctoral advisor was the prominent archaeologist, Bruce Trigger.

4:30 – A paper by Dr. Chrisomalis and colleagues on the “cultural challenge” in the study of mathematical cognition.

9:50 – One of several papers by Alexander Marshack on Upper Paleolithic tally systems.

19:00 – Dr. Chrisomalis’s earlier book on numeral systems—written for a more specialist audience and encyclopedic in scope—can be found here.

20:10 – The Armenian and Georgian numeral systems.

23:00 – The term “subitizing,” from the Latin for 'sudden,' was introduced in this article by Kaufman et al. in 1949.

24:20 – Conventions for making tally marks vary across cultures, a fact which recently went viral.

33:50 – The ancient Roman abacus was different from abacuses used in Asia.

35:00 – A recent paper on the benefits of abacus training in India.

42:20 – A paper on frequency-dependent selection.

49:00 ­– An article about the Cherokee syllabary, which was invented by Sequoyah.

1:00:20 ­­– A numerical notation developed in the 20th century based on color, used for labeling electrical resistors.

1:09:00 ­­– Dr. Chrisomalis maintains two websites about different kinds of language: Glossographia & The Phrontistery. His personal website is here.

Dr. Chrisomalis’s end of show recommendations:

Where Mathematics Comes From, by George Lakoff & Rafael Núñez

Cultural Development of Mathematical Ideas, by Geoffrey Saxe

Numbers and the Making of Us, by Caleb Everett

Many Minds is a project of the Diverse Intelligences Summer Institute (DISI) (https://disi.org), which is made possible by a generous grant from the Templeton World Charity Foundation to UCLA. It is hosted and produced by Kensy Cooperrider, with creative support from DISI Directors Erica Cartmill and Jacob Foster, and Associate Director Hilda Loury. Our artwork is by Ben Oldroyd (https://www.mayhilldesigns.co.uk/). Our transcripts are created by Sarah Dopierala (https://sarahdopierala.wordpress.com/).

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