Floor 6 — Hall of Numerals · written.institute

The zero, and who has one

The floor's dividing line

Zero is the only thing on this floor that is genuinely difficult. A system that sums its signs never needs one: nothing is missing from MMXXVI, because nothing is positional. A system whose digits take meaning from their column cannot manage without a way to say this column is empty — and inventing a sign for nothing is a conceptual step, not a notational convenience.

It was taken at least twice, by people who never met: in South Asia, and in Mesoamerica.

Babylon shows the cost of getting halfway. It had place value from around 2000 BCE and no zero for well over a millennium, so a scribe wrote the digits and the reader supplied the magnitude from context. The oldest securely dated zero on this floor is neither Indian nor Maya: it is a dot on a Khmer inscription of 683 CE. See Khmer, Maya and Babylonian.

Additive Hall

5 systems

Signs are summed. No columns, so no empty column to mark — and no zero.

Ⅰ Ⅴ Ⅹ Ⅼ Ⅽ Ⅾ Ⅿ Roman numerals base 10 · no zero · living 𓏺 𓎆 𓍢 𓆼 Egyptian numerals base 10 · no zero · historic α ́ β ́ γ ́ δ ́ ε ́ Greek numerals base 10 · no zero · living а ҃ в ҃ г ҃ д ҃ Cyrillic numerals base 10 · no zero · historic ፩፪፫፬፭፮፯፰፱ Ethiopic numerals base 10 · no zero · living

Positional Hall

13 systems

A digit's value depends on where it sits. Needs a zero to hold an empty place.

The Naming Hall

2 systems

Digit times named power, written the way the number is said.

一二三四五六七八九十 Chinese numerals base 10 · has zero · living 一二三四五六七八九十 Japanese numerals base 10 · has zero · living

Digits in use

All 20, one line each

System	Structure	Base	Zero	Status
Devanagari numerals	positional	10	yes	living
Arabic-Indic numerals	positional	10	yes	living
Roman numerals	additive	10	—	living
Babylonian numerals	positional	60	—	historic
Maya numerals	positional	20	yes	historic
Egyptian numerals	additive	10	—	historic
Greek numerals	additive	10	—	living
Cyrillic numerals	additive	10	—	historic
Ethiopic numerals	additive	10	—	living
Chinese numerals	multiplicative	10	yes	living
Japanese numerals	multiplicative	10	yes	living
Tamil numerals	positional	10	yes	living
Bengali numerals	positional	10	yes	living
Telugu numerals	positional	10	yes	living
Kannada numerals	positional	10	yes	living
Malayalam numerals	positional	10	yes	living
Thai numerals	positional	10	yes	living
Khmer numerals	positional	10	yes	living
Burmese numerals	positional	10	yes	living
Tibetan numerals	positional	10	yes	living

This floor holds numeral systems — sets of digits that mean by sequence and position. Standalone quantity marks that mean on their own, including the currency signs and the number sign, are read at symbolic.institute.