The numerical system

5.1 Credence in bits of log-odds

Core. Let p be the credence in the proposition currently being asserted. Define:

b = log₂(p / (1 − p)).

The inverse is:

p = 2ᵇ / (1 + 2ᵇ) = 1 / (1 + 2⁻ᵇ).

Positive b favors the proposition; negative b favors its negation. Zero gives equal odds. These are bits of log-odds, not binary digits in a probability and not the surprisal −log₂(p).

These numerical meanings are exact in the grammar. Their application to a real belief may be approximate, as specified below. A fluent speaker need not compute a decimal expansion each time; the odds interpretation is sufficient.

5.2 Finite near-certainty with av

Core. Av is associated by the design with avade, “of course/certainly,” but its numerical meaning is coined:

av repeated n times = +10n bits, for positive integer n.

Thus av, avav, and avavav mean +10, +20, and +30 bits. Each repetition multiplies the odds by 1,024. It does not multiply the probability by 1,024 and does not square the existing bit value.

For the negative side, un-av, un-avav, and un-avavav mean −10, −20, and −30 bits. The spelling keeps one negative prefix over the complete repeated magnitude.

ef-avavav=pon is emphatic and mathematically finite. It assigns the complement probability 1 / (1 + 2³⁰). “As close as language can get to certain” is not its literal meaning: the language permits another finite repetition or another explicitly written finite number.

5.3 Zero bits is allowed

The empirical prohibition on p = 0 or p = 1 does not prohibit the number zero elsewhere. ef⁰=pon is well formed and means p = 1/2. Δb = 0 means the evidence leaves the odds unchanged. Counts, utilities, and formal equations may also contain zero.

Equal odds do not automatically represent ignorance. Assigning 1/2 to every named alternative can be incoherent when there are three or more mutually exclusive possibilities. A speaker who has not formed a credence should suspend judgment explicitly rather than use nu as a generic “I don't know.”

5.4 Fractions, approximation, and ranges

Proposed. Finite real bit values are permitted, not just integers. For example, b = +1/2 gives odds √2:1 and p ≈ 0.5858. In speech, use the regular fraction expression after the sign: oy-brukh eyn iber tsve for +1/2, or the decimal oy-nu punkt fin. Written decimal or fraction notation is permitted for practical precision.

Three registers make the precision commitment explicit:

Shats is a proposed estimator flag associated with shatsn, “estimate.” The range is a report of the speaker's unresolved credence range, not automatically a Bayesian credible interval over an objective parameter. A parameter interval requires its own model and coverage statement. Approximation never licenses a missing number in an assertion.

5.5 Several alternatives

Proposed technical convention. A bare b-value concerns a proposition against its complement. Pairwise comparison of hypotheses must name both: b(H₁:H₂) = log₂(P(H₁)/P(H₂)). This is not necessarily H₁ against everything else.

For a mutually exclusive, exhaustive set of hypotheses, use a probability vector whose entries sum to one, or log-weights with explicit normalization. If weights are wᵢ, then P(Hᵢ) = 2ʷⁱ / Σⱼ2ʷʲ. These weights may all be shifted by the same constant without changing the probabilities. They are not independent binary credences that can be assigned arbitrarily.

The language can discuss an omitted “other” hypothesis. It should not make a set exhaustive merely by giving the named entries confident-sounding words.

5.7 The short digit roots

Core numeral standard. Use ten fixed, monosyllabic digits derived from Yiddish. These are constructed abbreviations, not claims about historical pronunciation. Most source forms are already one syllable in relevant pronunciations; the aim is to shorten clusters and remove irregular variants without sacrificing too much distinctiveness. The source forms from one through nine can be checked in YiddishPOP's number lesson.

The set preserves more than minimum syllable length. Keeping fir avoids a fragile fi/fin distinction based only on a final nasal. Tsve remains distinct from tsen “ten”; its v must be audible. All digits have one vowel nucleus, including the diphthongs in eyn and nay. The stated pronunciations are targets for this conlang, not a prohibition on ordinary accent variation.

Nu is also recognizable as an interjection. Numerical syntax disambiguates it: ef-nu=pon assigns even odds, while fil nu! is expressive content. If listeners find that overlap troublesome, nul is an obvious candidate replacement; it is not a second freely alternating numerical standard in Version 0.

Etlekh / עטלעך is an invariant approximate quantifier meaning “several,” not an extra digit. Etlekh tsen milyard expresses “tens of billions” without fixing a coefficient. Exact cardinal expressions still use the digit and scale rules below.

Digits never inflect for case, gender, position before a noun, or numerical environment. Eyn is one in isolation and before a noun. There is no special “two” form before hundreds or nouns. Clipping applies to these lexical numerals, not to every word ending in the same sounds.

5.8 Decimal composition from tens to thousands

The organizing idea is coefficient before place value, remainder after it. Twenty is “two ten”; twenty-three is “two ten three.” This borrows the transparent tens pattern exemplified by Mandarin 二十 and 二十三; the complete rules below are Yuddish's own, rather than a claim to reproduce every Chinese counting convention. See this Mandarin tens explanation.

The one-syllable requirement concerns digits zero through nine. A larger scale name may be longer. The named large scales follow powers of a thousand; the language borrows “two ten” without also requiring a ten-thousand grouping system.

A coefficient multiplies the scale immediately following it. Terms on descending scales add. Within a three-digit block, nonzero hundreds and tens have digit coefficients. A units digit has no scale word. There is no inherited units-before-tens inversion and no special teen series.

Leading-one rule: at the start of a three-digit coefficient block, omit eyn before tsen for 10–19. After a spoken hundred, keep it: 110 is eyn hund eyn tsen. Before hund, toyz, mil, or milyard, the coefficient is always explicit. A careful mathematical reading may restore the optional leading eyn before an initial tsen, but the table gives the canonical short form.

Hyphens may bind the parts visually: tsve-tsen-dra / צװע־צען־דראַ. They do not change the arithmetic. Do not shorten 23 to tsve dra: without a place word, that is a digit sequence, not the cardinal quantity.

5.9 Zero and omitted places

Nu alone denotes zero. In a cardinal numeral, insert one nu when one or more zero decimal places separate two spoken nonzero positions. Consecutive empty places share that one marker. Leading and trailing zero places are not read out in a cardinal. The rule makes the difference between 101 and 110 audible.

Build large numbers as nonzero blocks of up to three digits, each followed by its large scale, in descending order. Apply the gap rule both within blocks and across their boundaries: compare the last nonzero decimal position in the higher block with the first nonzero position in the lower block. An entirely empty block is omitted, with nu marking the resulting internal gap once. Thus 100,100 is eyn hund toyz nu eyn hund, and 1,001,100 is eyn mil nu eyn toyz eyn hund.

In a digit sequence, every zero is spoken separately. Write the constructor tsifer( … ) when clarity is needed. The identifier 007 is tsifer(nu nu zib), while the cardinal seven is zib. A serial code's leading zero has meaning even though a quantity's leading zero does not.

5.10 Fractions, decimal points, and mathematical notation

Decimal point: punkt / פּונקט. Read the integer part as a cardinal and every digit after the point separately. Thus 0.05 is nu punkt nu fin; 2.375 is tsve punkt dra zib fin; 20.04 is tsve tsen punkt nu fir. A trailing zero may be pronounced to preserve the stated measurement precision, while recognizing that 0.50 and 0.5 are the same real number.

Fraction constructor: brukh(A; B), read brukh A iber B, means A divided by nonzero B. For example, 3/20 is brukh dra iber tsve tsen. Parentheses or explicit grouping separate compound numerators and denominators; a complex nested expression should not rely on a pause alone. The fraction noun is invariant. Ordinary a halb “a half” may remain an idiom; formal bit readings use the regular fraction constructor.

Signed quantities: outside the established epistemic complex, use minus N and, where necessary, plus N. A strength attached to EF retains un-N and oy-N, respectively. Canonical zero is unsigned. Thus ef-un-dra=pon and ef⁻³=pon mean the same thing; an arithmetic expression may say minus dra.

Ratios and percentages: A:B is A tsu B, with the two terms explicitly identified when context is ambiguous. A percent is N protsent, N divided by 100. Neither notation assigns a probability unless the surrounding expression makes it one. Formal expressions can use exact rational numbers without claiming empirically exact measurements.

Powers and scientific notation: use the technical constructor pot(A; N), read A pot N, for A raised to N; pot is a proposed technical clipping associated with “power/potency.” A number such as 6.02 × 10²³ reads zek punkt nu tsve mol tsen pot tsve tsen dra. Parentheses fix scope in nested powers. This also supplies a systematic way to express magnitudes beyond the named scales without inventing an endless dictionary of large-number words.

5.11 Ordinals and counted nouns

The digits have no ordinal declensions. Use the invariant ordinal marker rang / ראַנג plus the cardinal numeral: dos probe rang tsve, “the second test,” and dos kapitel rang tsve tsen dra, “chapter twenty-three.” The label fixes an ordering or index; it does not multiply anything. Attributive modifiers stay invariant around numerals.

Counts use the same numeral forms: eyn model, tsve modeln, tsve tsen dra modeln. Number agreement follows the counted noun phrase: Dos tsve modeln efn⁺³=pon arbetn, “the two models work, +3 bits, by inference.” For frequency, N mol means N times and does not change the numeral's form.

5.12 Counting and credence remain separate

Ordinary counting is decimal; epistemic strength is measured in base-2 log-odds. The two choices are compatible, just as a decimal numeral can count bits in a computer memory. Written +20 bits therefore reads oy-tsve-tsen, and still means odds of 2²⁰:1.

The table omits evidentials only to show the numerical morphology; actual assertions still need a clitic. The repeated av forms keep their exact earlier meanings. They do not become alternate words for the probabilities 10%, 20%, or 30%.

For an explicitly binary digit string, use binar( … ) with only nu and eyn. Binary 101 reads binar(eyn nu eyn) and denotes decimal five, fin. Untagged mathematical numerals retain decimal interpretation. Digit-sequence, binary, fraction, and power constructors form numerical expressions; they are not new speech acts and do not bypass the assertion grammar.

5.13 Why this numerical system

This design keeps the roots recognizable while regularizing composition. It removes the separate vocabulary burden of teens and tens, retains exact decimal digits where measurement precision matters, and uses the same number words inside and outside credence expressions. Zero has a defined role rather than serving as a vague filler.

There are audible tradeoffs: fir/fin differ in their final consonant, nu overlaps with an interjection, and repeated place words can be long for enormous integers. These are candidates for listening tests, not reasons to leave the grammar unspecified. The digit set and composition rules above are the current proposal to test together.