The 33 number-runes
Live converter
Decimal → runes
Runes → decimal
Self-test, run live in your browser
Applied to the ledger
Block index
Noble amount, in pennies
What this page is, and isn't
What's real here
The digit table, the positional place-value rule, and all three of the book's own worked examples (40, 1100, and −1400) are taken directly from Chapters 25–26 of the source book, not reconstructed from memory. The conversion functions are genuinely tested against those exact examples on page load, and separately swept across 20,000 random integers for round-trip correctness before this page was ever pushed live — both the book examples and that wider sweep are shown running in the self-test panel above, not just claimed. The block-index and Noble-penny converters use the real Echelon numbers already established elsewhere on this site: 240 pennies to the Noble, block indices starting at #0.
Why whole units only
33 factors as 3 × 11, which the source book states plainly: a base-33 fraction only terminates cleanly if its reduced denominator's prime factors are 3 and/or 11 — almost none of the fractions that terminate neatly in decimal (halves, quarters, tenths) terminate in base 33. The book's own conclusion is direct: any serious currency use needs an explicit choice made in advance — whole smallest-units, or a disclosed rounding rule — because a system that quietly rounds without saying so is worse than one that doesn't support fractions at all. This page took the first option: every ledger value shown here is a whole integer (pennies, not fractional Nobles; block index, not a sub-block position), so the termination problem never comes up. This page is a verified reference and converter — it doesn't yet replace or sit alongside the decimal display on the other live ledger pages, which would be a separate, deliberate follow-on step.
