{"id":78874,"date":"2025-11-11T23:28:43","date_gmt":"2025-11-12T04:28:43","guid":{"rendered":"https:\/\/world.edu\/?p=78874"},"modified":"2025-11-11T23:28:43","modified_gmt":"2025-11-12T04:28:43","slug":"how-number-systems-shape-our-thinking-and-what-this-means-for-learning-language-and-culture","status":"publish","type":"post","link":"https:\/\/world.edu\/how-number-systems-shape-our-thinking-and-what-this-means-for-learning-language-and-culture\/","title":{"rendered":"How number systems shape our thinking, and what this means for learning, language and culture"},"content":{"rendered":"

\"\"<\/p>\n

Most of us have little trouble working out how many millilitres are in 2.4 litres of water (it\u2019s 2,400). But the same can\u2019t be said when we\u2019re asked how many minutes are in 2.4 hours (it\u2019s 144).<\/p>\n

That\u2019s because the Indo-Arabic numerals we often use to represent numbers are base-10, while the system we often use to measure time is base-60.<\/p>\n

Expressing time in decimal notation leads to\u00a0an interaction between these two bases<\/a>, which can have implications at both the cognitive and cultural level.<\/p>\n

Such base interactions and their consequences are among the important topics covered in a\u00a0new issue of the Philosophical Transactions of the Royal Society<\/em> journal<\/a>, which I co-edited with colleagues Andrea Bender (University of Bergen), Mary Walworth (French National Centre for Scientific Research) and Simon J. Greenhill (University of Auckland).<\/p>\n

The themed issue brings together work from anthropology, linguistics, philosophy and psychology to examine how humans conceptualize numbers and the numeral systems we build around them.<\/p>\n

What are bases, and why do they matter?<\/strong><\/h4>\n

Despite using numeral bases on a daily basis, few of us have reflected on the nature of these cognitive tools. As I explain in\u00a0my contribution to the issue<\/a>, bases are special numbers in the numeral systems we use.<\/p>\n

Because our memories aren\u2019t unlimited, we can\u2019t represent each number with its own unique label. Instead, we use a small set of numerals to build larger ones, like \u201cthree hundred forty-two.\u201d<\/p>\n

That\u2019s why most numeral systems are structured around a\u00a0compositional anchor<\/a>\u00a0\u2014 a special number with a name that serves as a building block to form names for other numbers. Bases are anchors that exploit powers of a special number to form complex numerical expressions.<\/p>\n

The English language, for example, uses a decimal system, meaning it uses the powers of 10 to compose numerals. So we compose \u201cthree hundred and forty-two\u201d using three times the second power of 10 (100), four times the first power of 10 (10) and two times the zeroth power of 10 (one).<\/p>\n

This base structure allows us to represent numbers of all sizes without overloading our cognitive resources.<\/p>\n

Languages affect how we count<\/strong><\/h4>\n

Despite the abstract nature of numbers, the degree to which numeral systems transparently reflect their bases has very concrete implications \u2014 and not just when we tell time. Languages with less transparent rules will take longer to learn, longer to process and can lead to more calculation and dictation errors.<\/p>\n

Take French numerals, for example. While languages like French, English and Mandarin all share the same base of 10, most dialects of French have what could politely be called a\u00a0quirky way of representing numbers in the 70-99 range<\/a>.<\/p>\n

Seventy is\u00a0soixante-dix<\/em>\u00a0in French, meaning \u201csix times 10 plus 10,\u201d while 80 uses 20 as an anchor and becomes\u00a0quatre-vingts<\/em>, meaning \u201cfour twenties\u201d (or \u201cfour twenty,\u201d depending on the context). And 90 is\u00a0quatre vingt dix<\/em>, meaning \u201cfour twenty ten.\u201d<\/p>\n

French is far from being alone in being quirky with its numerals.\u00a0In German<\/a>, numbers from 10 to 99 are expressed with the ones before the tens, but numbers over 100 switch back to saying the largest unit first.<\/p>\n

Even in English, the fact that \u201ctwelve\u201d is said instead of \u201cten two\u201d hides the decimal rules at play. Such irregularities spread far beyond languages.<\/p>\n

How bases shape learning and thought<\/strong><\/h4>\n

Base-related oddities are\u00a0spread out across the globe<\/a>\u00a0and have very real implications for\u00a0how easily children learn what numbers are and how they interact with objects such as blocks<\/a>, and for\u00a0how efficiently adults manipulate notations<\/a>.<\/p>\n

For example,\u00a0one study found<\/a>\u00a0that lack of base transparency slows down the acquisition of some numerical abilities in children, while another found similar negative effects on how quickly they\u00a0learn how to count<\/a>.<\/p>\n

Another study<\/a>\u00a0found that children from base-transparent languages were quicker to use large blocks worth 10 units to represent larger numbers (for example, expressing 32 using three large blocs and two small ones) than children with base-related irregularities.<\/p>\n

While Mandarin\u2019s perfectly transparent decimal structure can simplify learning,\u00a0a new research method<\/a>\u00a0suggests that children may find it easier to learn what numbers are if they are exposed to systems with compositional anchors that are smaller than 10.<\/p>\n

In general, how we represent bases has very concrete cognitive implications, including\u00a0how easily we can learn number systems<\/a>\u00a0and\u00a0which types of systems will tend to be used in which contexts<\/a>.<\/p>\n

At a cultural level, base representation influences our ability to collaborate with scientists across disciplines and across cultures. This was starkly illustrated by the infamous Mars Climate Orbiter incident, when a mix-up between metric and imperial units\u00a0caused a $327 million spacecraft to crash into Mars in 1999<\/a>.<\/p>\n

Why understanding bases matters<\/strong><\/h4>\n

Numeracy \u2014 the ability to understand and use numbers \u2014 is\u00a0a crucial part of our modern lives<\/a>. It has implications for our quality of life and for our ability to make informed decisions in domains like\u00a0health and finances<\/a>.<\/p>\n

For example, being more familiar with numbers will influence how easily we can choose between retirement plans, how we consider trade-offs between side-effects and benefits when choosing between medications or how well we understand how probabilities apply to our investments.<\/p>\n

And yet many struggle to learn what numbers are, with millions suffering from\u00a0math anxiety<\/a>. Developing better methods for helping people learn how to manipulate numbers can therefore help millions of people improve their lives.<\/p>\n

Research on the cognitive and cultural implications of bases collected in the\u00a0Philosophical Transactions of the Royal Society<\/em>\u00a0journal can help make progress towards our understanding of how we think about numbers, marking an important step towards making numbers more accessible to everyone.<\/p>\n

Author Bio:<\/strong> Jean-Charles Pelland is a Postdoctoral Researcher, Department of Psychosocial Science at the University of Bergen<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Most of us have little trouble working out how many millilitres are in 2.4 litres of water (it\u2019s 2,400). But the same can\u2019t be said when we\u2019re asked how many minutes are in 2.4 hours (it\u2019s 144). That\u2019s because the Indo-Arabic numerals we often use to represent numbers are base-10, while the system we often […]\n… learn more→<\/a><\/p>","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[15645],"tags":[435573],"coauthors":[11733],"class_list":["post-78874","post","type-post","status-publish","format-standard","hentry","category-education","tag-numeral-bases"],"acf":[],"yoast_head":"\nHow number systems shape our thinking, and what this means for learning, language and culture - World leading higher education information and services<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/world.edu\/how-number-systems-shape-our-thinking-and-what-this-means-for-learning-language-and-culture\/\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:locale\" content=\"en_US\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:type\" content=\"article\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:title\" content=\"How number systems shape our thinking, and what this means for learning, language and culture - World leading higher education information and services\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:description\" content=\"Most of us have little trouble working out how many millilitres are in 2.4 litres of water (it\u2019s 2,400). 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