Rēgēs Inter Rēgulās: Even Better Roman

Pyrrha Pulcheria Titania Maxima Candida, Þн.δ.

While I applaud the stated (and admirably well-hyphenated) goal of P. G. Cognomen in his otherwise somewhat meandering article, “Numeri++” (SpecGram CLXXX.3, 2018)—namely, to improve “humanities-nerd–science-nerd relations” by “convinc[ing] the STEMmier nerds that linguistics is at least kinda interesting”—I am nonetheless disturbed that Cognomen has fallen victim to one of the classic blunders—the most famous of which is “never argue with anyone who buys the ink by the barrel!”, but only slightly less well-known is this: “never fail to capture a generalization!” (See, for example, “Another Horrifying Cliché,” from Lingua Pranca, 1978—now that’s classic!)

Cognomen, in fn. †, defines an “increment function” (add “I” to the end of the previous Roman number) and three sets of rewrite rules:

These rules will get you up to the “maximum” standard Roman numeral, MMMCMXCIX (3,999), but once you introduce the apostrophus (ↁ) or vinculum (V̅) to go beyond 4,000, the need for additional specific rules rears its ugly head.

Of course, there is an obvious abstract generalization to the rules to be made, after we introduce just a little bit of handy notation to represent abstract collections of 1-based units and 5-based hands:

U = “unit” or 1× symbol (I, X, C, M, X̅/ↂ, C̅/ↈ)
U_i = 1×10ⁱ
U₀ = I; U₁ = X; U₂ = C; U₃ = M; U₄ = X̅ or ↂ; etc.

H = “hand” or 5× symbol (V, L, D, V̅/ↁ, L̅/ↇ, D̅)
H_i = 5×10ⁱ
H₀ = V; H₁ = L; H₂ = D; H₃ = V̅ or ↁ; etc.

The Cyclic Generalized Roman Numeral Rewrite Rules follow immediately:

• U_iU_iU_iU_i → U_iH_i / ____#
• U_iH_iU_i → H_i / ____#
• H_iU_iH_i → U_iU_{i + 1} / ____#
• U_iU_{i + 1}U_i → U_{i + 1} / ____#

If we introduce one more abstract symbol for 2-based duals...

Ꙫ = “dual” or 2× symbol (J, Y, G, N, Y̅, G̅)
Ꙫ_i = 2×10ⁱ
Ꙫ₀ = J; Ꙫ₁ = Y; Ꙫ₂ = G; Ꙫ₃ = N; etc.

...then Cognomen’s (unstated!) Numeri++ Rewrite Rules can be Generalized thusly:

• U_iU_i → Ꙫ_i / ____#
• Ꙫ_iꙪ_iU_i → H_i / ____#
• H_iH_i → U_{i + 1} / ____#

Cognomen’s own comment on his original Roman Numeral Rewrite Rules still ring true:

Honestly, it seems pretty straightforward when you look at it like this... This also goes to show that most subjects are amenable to linguisticky interpretation if you look hard enough. Ah, Linguistics! Is there anything it can’t do!?

Id est factum, Iōannēs!

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