@cite{woodin-etal-2023}: Numeral Frequency and Roundness

@cite{sigurd-1988} @cite{woodin-etal-2023}

Corpus study showing number frequency is predicted by: (a) log magnitude, and (b) graded roundness via Sigurd/Jansen & Pollmann k-ness properties.

Key finding: each k-ness property has an independent positive effect on frequency, with 10-ness being the strongest predictor and multipleOf5 the weakest.

Register Effect

Informational texts (Wikipedia) show stronger roundness effects than non-informational texts (fiction, conversation), suggesting roundness interacts with communicative goals.

structure Phenomena.Numerals.Studies.WoodinEtAl2024.RoundnessCoefficient : Type

Regression coefficient for each k-ness property on log frequency.

Higher β = stronger positive effect on numeral frequency in corpora. All coefficients are positive: each property independently increases frequency.

• property : String
• β : ℚ

instance Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRoundnessCoefficient : Repr RoundnessCoefficient

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRoundnessCoefficient = { reprPrec := Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRoundnessCoefficient.repr }

def Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRoundnessCoefficient.repr : RoundnessCoefficient → ℕ → Std.Format

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def Phenomena.Numerals.Studies.WoodinEtAl2024.β_tenness : RoundnessCoefficient

β coefficients ordered by magnitude (Table 3).

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.β_tenness = { property := "10-ness", β := 446 / 100 }

def Phenomena.Numerals.Studies.WoodinEtAl2024.β_2_5ness : RoundnessCoefficient

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.β_2_5ness = { property := "2.5-ness", β := 384 / 100 }

def Phenomena.Numerals.Studies.WoodinEtAl2024.β_5ness : RoundnessCoefficient

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.β_5ness = { property := "5-ness", β := 261 / 100 }

def Phenomena.Numerals.Studies.WoodinEtAl2024.β_2ness : RoundnessCoefficient

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• Phenomena.Numerals.Studies.WoodinEtAl2024.β_2ness = { property := "2-ness", β := 156 / 100 }

def Phenomena.Numerals.Studies.WoodinEtAl2024.β_mult10 : RoundnessCoefficient

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.β_mult10 = { property := "multipleOf10", β := 52 / 100 }

def Phenomena.Numerals.Studies.WoodinEtAl2024.β_mult5 : RoundnessCoefficient

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.β_mult5 = { property := "multipleOf5", β := 6 / 100 }

def Phenomena.Numerals.Studies.WoodinEtAl2024.roundnessHierarchy : List RoundnessCoefficient

The 6 coefficients in descending order.

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theorem Phenomena.Numerals.Studies.WoodinEtAl2024.hierarchy_ordering : β_tenness.β > β_2_5ness.β ∧ β_2_5ness.β > β_5ness.β ∧ β_5ness.β > β_2ness.β ∧ β_2ness.β > β_mult10.β ∧ β_mult10.β > β_mult5.β

def Phenomena.Numerals.Studies.WoodinEtAl2024.weightedRoundnessScore (n : ℕ) : ℚ

Frequency-weighted roundness score using Woodin et al.'s β coefficients.

Unlike the unweighted roundnessScore (which counts properties equally), this weights each property by its empirical frequency effect.

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theorem Phenomena.Numerals.Studies.WoodinEtAl2024.weighted_100_gt_50 : weightedRoundnessScore 100 > weightedRoundnessScore 50

theorem Phenomena.Numerals.Studies.WoodinEtAl2024.weighted_50_gt_110 : weightedRoundnessScore 50 > weightedRoundnessScore 110

theorem Phenomena.Numerals.Studies.WoodinEtAl2024.weighted_7_eq_zero : weightedRoundnessScore 7 = 0

inductive Phenomena.Numerals.Studies.WoodinEtAl2024.Register : Type

Register type from corpus analysis.

Informational registers (Wikipedia) show stronger roundness effects than non-informational registers (fiction, conversation).

• informational : Register
• nonInformational : Register

def Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRegister.repr : Register → ℕ → Std.Format

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instance Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRegister : Repr Register

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• Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRegister = { reprPrec := Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRegister.repr }

instance Phenomena.Numerals.Studies.WoodinEtAl2024.instDecidableEqRegister : DecidableEq Register

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.instDecidableEqRegister x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Numerals.Studies.WoodinEtAl2024.instBEqRegister : BEq Register

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.instBEqRegister = { beq := Phenomena.Numerals.Studies.WoodinEtAl2024.instBEqRegister.beq }

def Phenomena.Numerals.Studies.WoodinEtAl2024.instBEqRegister.beq : Register → Register → Bool

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.instBEqRegister.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

structure Phenomena.Numerals.Studies.WoodinEtAl2024.RegisterEffectDatum : Type

Register effect datum: roundness β is larger in informational texts.

• register : Register
• roundnessEffectMagnitude : String
• notes : String

instance Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRegisterEffectDatum : Repr RegisterEffectDatum

Equations

• Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRegisterEffectDatum = { reprPrec := Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRegisterEffectDatum.repr }

def Phenomena.Numerals.Studies.WoodinEtAl2024.instReprRegisterEffectDatum.repr : RegisterEffectDatum → ℕ → Std.Format

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def Phenomena.Numerals.Studies.WoodinEtAl2024.informationalEffect : RegisterEffectDatum

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def Phenomena.Numerals.Studies.WoodinEtAl2024.nonInformationalEffect : RegisterEffectDatum

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