Zero Speculation

Introduction: The Standard Story and Its Gaps

The story of zero as commonly told runs: emptiness as Buddhist philosophy (śūnyatā, c. 3rd century BCE) → placeholder dot in calculation (śūnya-bindu, Bakhshali manuscript, 3rd–4th century CE) → arithmetic zero with defined rules (Brahmagupta, Brahmasphutasiddhānta, 628 CE) → stone inscription zero (Gwalior temple, 876 CE).

Amir Aczel's Finding Zero (2015) added a crucial chapter: the earlier Khmer inscription K-127 (683 CE), bearing a zero in positional notation predating the Gwalior zero by nearly two centuries. Aczel's quest — recovering the stone from Phnom Penh — dramatised the question of where the zero symbol originated before reaching Cambodia.

The Etymology of Śūnya: Sanskrit or Dravidian?

2.1 The standard internal Sanskrit derivation

Sanskrit śūnya is conventionally derived from the root śvi / śū- (to swell, to be hollow), giving śū-na (hollow, swollen) → śūnya (empty, void). The proposed Proto-Indo-European cognate *ḱeu- (to swell) links to Greek κύω and English swollen — but this connection is weak and contested. Mayrhofer's authoritative Etymologisches Wörterbuch des Altindoarischen (1992–2001) flags words without clean Indo-European cognates as candidates for Dravidian substrate influence.

2.2 The Dravidian cluster: suḻi, suḻiyam, sonne

The phonological path suḻi → śūnya would require: s → ś (palatalisation, common in Sanskrit contact); uḻ → ū (loss of retroflex lateral, vowel lengthening); -i → -ya (Sanskrit nominalising suffix applied to borrowed root). This is entirely within the documented patterns of Dravidian-to-Sanskrit phonological adaptation.

2.3 Chronological layering of śūnya

This layering is consistent with a word that entered Sanskrit from a Dravidian substrate at a mundane, concrete level, was then philosophically elaborated, and finally mathematised.

The Puḷḷi Hypothesis: Absence as Scribal Architecture

3.1 The Tamil puḷḷi and its uniqueness

The Tamil puḷḷi (புள்ளி, virama dot) is attested in inscriptions from the 2nd century CE (Mahadevan 2003, Early Tamil Epigraphy), making it one of the earliest explicit visible absence-markers in any South Asian script. It marks "no vowel follows this consonant" — a visible dot encoding positional absence within a structured system.

The word puḷḷi derives from pul- (small, insignificant, minimal) — cognate with Kannada hullu (grass, trivial, low). The puḷḷi is the smallest meaningful mark — the minimum perceptible unit. This is also what cukke means in Kannada: both "dot/point" and "star" (a dot of light in the distance).

3.2 The structural isomorphism

The Bakhshali manuscript zero (3rd–4th century CE) is a dot — graphically identical to the Tamil puḷḷi. The coincidence of form invites the hypothesis that the scribal tradition of marking positional absence as a dot migrated from phonological notation into numerical notation.

3.3 Why Tamil resisted positional zero

The Tamil numeral system retained dedicated glyphs for 10 (௰), 100 (௱), and 1000 (௲) and never natively adopted positional zero within a traditional framework. Modern Tamil ௦ is essentially a contemporary adoption. This is structurally parallel to Tamil's retention of the visible puḷḷi: both reflect a system that already had a rich infrastructure for encoding absence explicitly, and therefore had less need to import a new symbol.

Kannada, by contrast, handled the virama differently: consonant clusters were encoded through subjoined ligature stacking — the virama was hidden inside the conjunct form, invisible in the rendered glyph. The explicit halanta (್) became consistently visible in Kannada inscriptions only from the Rashtrakuta period (8th–10th century CE) — precisely when positional zero was also being adopted (~9th–10th century CE). The two innovations arrived together.

The Cambodia Connection: K-127 and the Pallava-Kadamba Debate

4.1 K-127 and its zero

Khmer inscription K-127, dated 683 CE (Śaka year 605), discovered at Sambor on the Mekong River, contains the earliest dated zero in stone. The numeral 605 is written with a positional zero in the hundreds place — unambiguous place-value notation. This antedates the Gwalior temple zero (876 CE) by nearly two centuries.

4.2 The script attribution controversy

The script of K-127 is conventionally attributed to "Pallava Grantha". However, the attribution is contested on several grounds:

• Epigrapher Arlo Griffiths prefers the term Late Southern Brāhmī for the cluster of related scripts, calling "Pallava" misleading.
• The earliest Pallava inscriptions (Mayidavolu copper plates, 4th century CE) use Kadamba script, not a distinct "Pallava" script. Grantha and Vatteluthu evolved from Kadamba.
• The Śaka era used in Cambodian and Indonesian inscriptions was introduced by the Chalukyas of Badami (Karnataka) — it was never used by the Pallavas.
• The "box-headed alphabet" in Champa (central Vietnam) inscriptions is "generally found in central and upper Deccan as well as Kannada-speaking areas," not in Pallava territory.

4.3 The Grantha-ottakṣara connection

Grantha script developed the ottakṣara — stacked subjoined consonant forms — which are structurally closer to the conjunct-stacking tradition of Kadamba/Kannada than to the Tamil-Brāhmī orthography. The Khmer script's handling of consonant clusters through subjoined forms is architecturally closer to this Kadamba-Grantha tradition than to the Tamil puḷḷi approach.

A direct dynastic connection also existed: after Pallava king Parameśvaravarman II died without heir (~730 CE), Pallavamalla (Nandivarman II) was the prince who returned from Cambodia to claim the Pallava throne. The Pallava-Cambodia-Kadamba triangle is genealogical, not merely scribal.

Synthesis: A Dravidian Archaeology of Zero

Assembling the evidence, we can sketch a speculative but coherent genealogy:

The Pūrṇam Adaḥ Paradox

The verse asserts that taking the full from the full leaves the full unchanged. This is structurally identical to the statement that ∞ − ∞ = ∞ — the infinite as an identity element under subtraction of itself.

What the verse does not say is: "the empty from the full leaves the full." But it implies it: if pūrṇa minus pūrṇa equals pūrṇa, then zero is the only number consistent with this arithmetic. The pūrṇa/śūnya polarity was the conceptual container that eventually had to be formalised arithmetically — and when it was, it produced the Hindu-Arabic numeral system that the world uses today.

Open Questions and Further Research

This essay has been speculative throughout. The following questions require philological and paleographic investigation before any of the hypotheses above can be treated as established.

1. DEDR entry for pul-/puḷ-: Does Burrow & Emeneau's Dravidian Etymological Dictionary contain entries that link puḷḷi (dot), puḷi (tiger, spotted), and pul (insignificant/small) to a reconstructed Proto-Dravidian root? The semantic coherence (minimal mark = spot on an animal = smallest unit) is suggestive but needs philological confirmation.
2. Śūnya in Mayrhofer: Does Mayrhofer's EWAia entry for śūnya flag the absence of IE cognates and mention any Dravidian parallel? If so, this would be the authoritative acknowledgement the hypothesis needs.
3. K-127 script paleography: A detailed comparative analysis of K-127's numeral glyphs — specifically the zero — against contemporary Kadamba, Grantha, and Tamil-Brāhmī numeral forms would clarify the script attribution question. The visual relationship between Gudnapur numerals and K-127 numerals deserves examination.
4. Virama appearance timeline in Kadamba: A systematic survey of Kadamba copper plate inscriptions for the first consistent appearances of explicit virama marks (versus implicit conjunct handling) would test the hypothesis that explicit absence-marking and zero adoption are correlated.
5. Tamil astronomical texts: Did Tamil astronomers (working with the Āryabhaṭīya tradition after ~499 CE) use the puḷḷi in numerical contexts, or did they switch to a separate zero symbol? The answer would clarify whether the puḷḷi was ever consciously identified with zero in Tamil scribal practice.