When a French speaker says "quatre-vingts" for 80, they're literally saying "four twenties." When a Dane says "halvtreds" for 50, they mean "half-third times twenty." And in the Amazon, the Pirahã people have no words for specific numbers at all. The way humans count varies far more than most people realize.
Number Bases: Not Everyone Uses Ten
Most modern languages use a decimal (base-10) system - likely because humans have ten fingers. But this isn't universal:
Most languages
French, Basque, Maya
Hours, months, inches
Minutes, seconds, degrees
Vigesimal (Base-20): Counting with Fingers AND Toes
Base-20 systems likely developed from counting all twenty digits - fingers and toes. This system appears across unrelated language families worldwide:
French preserves vigesimal traces from its Celtic (Gaulish) and Old Norse influences. While "trente" (30) and "quarante" (40) are straightforward decimal, the fun begins at 70:
| Number | French | Literal Meaning |
|---|---|---|
| 70 | soixante-dix | sixty-ten |
| 71 | soixante-et-onze | sixty-and-eleven |
| 80 | quatre-vingts | four-twenties |
| 90 | quatre-vingt-dix | four-twenties-ten |
| 99 | quatre-vingt-dix-neuf | four-twenties-ten-nine |
Belgian and Swiss French simplify this with "septante" (70), "octante/huitante" (80), and "nonante" (90) - but France keeps its mathematical workout.
Danish: Mathematical Madness
Danish takes vigesimal counting to another level with a system that confuses even Scandinavian neighbors:
| Number | Danish | Breakdown |
|---|---|---|
| 50 | halvtreds | (3 - ½) × 20 = 2.5 × 20 |
| 60 | tres | 3 × 20 |
| 70 | halvfjerds | (4 - ½) × 20 = 3.5 × 20 |
| 80 | firs | 4 × 20 |
| 90 | halvfems | (5 - ½) × 20 = 4.5 × 20 |
The "halv-" prefix means "half before," so "halvtredje" literally means "half of the third (twenty)" or 2½ twenties. It's mathematically correct but cognitively demanding.
Languages Without Numbers
Perhaps the most surprising discovery in linguistic research: some languages have no words for exact numbers at all.
The Pirahã People of Brazil
The Pirahã language has only three quantity words:
- hói - roughly "small amount" (one or two)
- hoí - roughly "somewhat larger amount"
- baagi - "many" or "much"
Studies show that Pirahã speakers can still perceive exact quantities - they simply don't lexicalize them. When asked to match quantities, they succeed with small numbers but increasingly approximate with larger ones.
Similarly, the Mundurukú of Brazil have words only for numbers one through five, with "many" for anything larger. Research suggests this isn't a cognitive limitation but a cultural choice - these societies simply haven't needed precise large numbers.
Different Digits: Writing Numbers Across Scripts
The "Arabic numerals" we use (0-9) actually originated in India and spread through Arab mathematicians to Europe. But many writing systems have their own digit characters:
Chinese, Japanese, and Korean use both their traditional characters and Arabic numerals, often choosing based on context:
| Number | Chinese | Japanese | Korean |
|---|---|---|---|
| 1 | 一 | 一 / いち | 一 / 하나 |
| 2 | 二 | 二 / に | 二 / 둘 |
| 3 | 三 | 三 / さん | 三 / 셋 |
| 10 | 十 | 十 / じゅう | 十 / 열 |
| 100 | 百 | 百 / ひゃく | 百 / 백 |
Counting Words: The Classifier System
In many East and Southeast Asian languages, you can't just say "three books" - you need a classifier word that categorizes what you're counting:
Japanese Counters
- 三本 (san-bon) - three long thin things (pens, bottles, trees)
- 三冊 (san-satsu) - three bound things (books, magazines)
- 三匹 (san-biki) - three small animals (dogs, cats, fish)
- 三羽 (san-wa) - three birds or rabbits
- 三台 (san-dai) - three machines or vehicles
Japanese has over 500 counter words, though about 30 cover most everyday situations.
Chinese, Thai, Vietnamese, and Malay-Indonesian languages use similar systems. This isn't just grammatical complexity - research suggests classifier languages may encourage different mental categorization of objects.
Grammatical Number: Beyond Singular and Plural
English distinguishes singular (one) from plural (more than one). But many languages have more distinctions:
| Category | Quantity | Languages |
|---|---|---|
| Singular | 1 | Universal |
| Dual | exactly 2 | Arabic, Slovene, Sanskrit |
| Trial | exactly 3 | Tok Pisin, some Oceanic |
| Paucal | few (3-10) | Arabic, Russian (2-4) |
| Plural | many | Universal (where present) |
Slovenian has six number forms for nouns! A book is "knjiga" (1), "knjigi" (2), "knjige" (3), "knjige" (4), and changes form again for 5+ with additional variations for cases.
Finger Counting: It's Not Universal Either
How do you show "three" with your fingers? If you're from Western Europe, probably index-middle-ring. But this varies culturally:
- Germany: Start with thumb (1), then thumb+index (2), etc.
- Japan: Start with an open palm (5), close fingers to count down
- China: Has a one-handed system to count to 10 using different finger positions
- Middle East: Often start counting on pinky finger
The German thumb-first system famously appears in the film "Inglourious Basterds," where an Allied spy's "wrong" finger counting reveals his non-German origin.
Key Insight
Number systems reveal deep truths about human cognition: numbers are not hardwired but culturally constructed. While the ability to perceive quantity may be innate, how we name, organize, and manipulate numbers is learned - and varies dramatically across human societies.
The Future: Will Number Systems Converge?
Globalization and international commerce have made the decimal system increasingly dominant. Scientific notation, computing, and international trade all favor base-10. Yet cultural number traditions persist:
- The French stubbornly keep quatre-vingts despite Belgian alternatives
- Japan uses traditional counters alongside Arabic numerals
- Many South Asian countries print local digits on currency and documents
Numbers, like languages, carry cultural identity. The way we count isn't just mathematics - it's heritage.