The metric is not carried by the symbol. It is imposed by the reader.
A research project investigating how number representation systems encode relational structure (order, correspondence, nesting) that is neutral with respect to the choice of metric — Archimedean or non-Archimedean (ultrametric).
The same symbolic configuration (e.g., 10, notches on a tally stick, knots on a quipu) can be interpreted under either:
- Archimedean valuation — real numbers, Euclidean distance, the familiar metric
-
Non-Archimedean (
$p$ -adic) valuation — ultrametric distance, the strong triangle inequality
The metric is a reader-imposed interpretative framework, not an inherent property of the representation.
- Georges Ifrah's Universal History of Numbers: Number systems are fossilized forms of cultural cognitive choices. The decimal system is an engineering solution, not a natural inevitability.
- Pre-numeric primitives (notches, beads, knots): Carry correspondence, order, and nesting — metric-neutral.
-
$p$ -adic number theory: Provides the mathematical framework for ultrametric valuation. - QWAV framework: Ultrametric quantum computing and AI; this project extends the ultrametric interpretation to the anthropology of number representation.
- Phase 0: Seed document and project scaffolding
-
Phase 1: Literature review — Ifrah,
$p$ -adic analysis, cognitive anthropology - Phase 2: Formal development — metric-neutral representation theory
- Phase 3: Applications and implications
- Phase 4: Publication
GitHub: qnfo/symbol-metric-neutrality
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