Preserved research collection

Sinhala numeration & the long history of zero

Research by Harsha Wijayawardhana on Sinhala Illakkam, Lith Illakkam, the zero placeholder, Brahmi-derived numeral forms and the extraordinary large-number vocabulary of the Pujavaliya.

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Research overview

Two Sinhala numeral traditions

Harsha’s research, begun in 2007 and published in the 2009 book Numeration in the Sinhala Language, drew on rock inscriptions, ola-leaf manuscripts, early Dutch and Portuguese publications and material in Sri Lankan museum collections. It distinguishes two related but functionally different numeral systems.

Sinhala Illakkam

An additive numeral system used by the Kandyan royal court and visible in the 1815 Kandyan Convention. It had signs for units and powers such as 10, 100 and 1,000, but no zero.

Lith Illakkam

A decimal place-value system used especially in astrology and ephemerides. It employed a zero placeholder and remained in practical use in horoscope calculation.

Brahmi inheritance

Both traditions are traced to Brahmi numeral forms recorded in Sri Lanka. Sinhala Illakkam retained an additive structure, while Lith Illakkam developed decimal notation.

Unicode preservation

Sinhala Illakkam and Lith Illakkam were encoded in Unicode, preserving the ability to represent both historical systems digitally.

The Sinhala zero

Ola manuscripts on astrology show a zero placeholder associated with the hal lakuna or halanta. The research argues that Sri Lankan astrologers used place-value notation in addition, subtraction, multiplication and division by at least the early eighteenth century. It also explores an earlier hypothesis: that the nullifying function of the halanta in Sinhala writing and the placeholder function of zero may reflect a related conceptual history. The Menikdena brick marks described in the research are presented as suggestive evidence requiring further archaeological study—not as a settled identification.

The distinction between śūnya as emptiness and binduwa as a numerical zero becomes especially important in the Pujavaliya. The text appears to use the latter in a specifically quantitative comparison, supporting the argument that zero was understood independently as a number.

Pujavaliya · 13th century

Large numbers beyond a googol

The Pujavaliya, attributed to Buddhaputhra Sthavira of Mayurapada Pirivena and composed during the Dambadeniya period, defines and uses an extended sequence of number names. In the Sinhala sequence recorded in the article, each major step after koti advances by seven decimal powers, reaching asamkhaya at 10133—far beyond a googol, 10100.

Name recorded in SinhalaPower of tenIndic comparison recorded in the article
Seeya — hundred102Hundred
Dahasa — thousand103Sahasra
Laksha — hundred thousand105Laksa
Koti — ten million107Koti
Prakoti1014Pakoti
Koti-prakoti1021Kotippakoti
Nahuthaya1028Nahuta
Ninnahuthaya1035Ninnahuta
Huthanahuthaya1042Akkhobini
Kambha1049Bindu
Wiskambhaya1056Abbuda
Ahahayaka1063Nirabbuda
Ababayaka1070Ahaha
Atatayaka1077Ababa
Sogandiyaka1084Atata
Upapalyaka1091Sogandhika
Kumuduyaka1098Uppala
Pundariyaka10105Kumuda
Padumayaka10112Pundarika
Kathanayaka10119Paduma
Mahakathanayaka10126Kathana
Asamkhaya10133Mahakathana; the wider Indian sequence places Asamkhaya at 10140

Binduwa as number

To convey the immensity of asamkhaya, the Pujavaliya compares it with stars, ocean water, the earth’s soil and a hypothetical Mount Meru pulverised into mustard-seed-sized particles. The final quantity is described as still falling short by a binduwa. Harsha reads this as evidence that the author distinguishes voidness from a zero-valued number and that learned ganithayas worked with both enormous quantities and infinitesimal comparisons.

The article relates this language to the modern idea of approaching zero. That is best read as a historical interpretation and conceptual parallel; it does not by itself establish a formal medieval theory identical to modern differential or integral calculus.

Talks and explanations

Numeration media archive

Journey through time: Searching for the Zero

A Sinhala-language survey of the historical search for zero.

Linguistic Zero

The relationship between absence, language and number.

Indian Brahmi Numerals

The development and regional context of Brahmi numeral forms.

Brahmi and Pocket Watch

A concise visual explanation from the continuing research series.