Universal #1368

Legacy number: 1368

 Number  1364
 Original  In systems with more than one base, there is a base, the base for predictable explanation, above which in all numerals certain regularities hold. Such numerals, when analyzed into their two principal constituents, will fall into two types, simple and complex. In the simple numeral we have a product, or rarely a quotient. In the complex numeral the two constituents are summands.
In the simple constituent the factors or elements in a division are expressed in the same way as when they occur in isolation. Complex expressions fall into two parts, a product and a remainder.
The remainder has the two following properties. It never has a larger value than the next lower base of the total expression. Finally, the remainder is expressed by the same mathematical function as when it occurs in isolation.
 Standardized  IF there are numeral systems with more than one base, THEN there is a base, the base for predictable explanation, above which in all numerals certain regularities hold. Such numerals, when analyzed into their two principal constituents, will fall into two types: simple (A) and complex (B) ones:

<table class = "textTable">

<tr>

<td> </td>

<td>(Ai)</td>

<td colspan="2"> In the simple numeral we have a product, or rarely a quotient.</td>

</tr>

<tr>

<td> </td>

<td valign="top">(Aii)</td>

<td colspan="2">In the simple constituent the factors or elements in a division are expressed in the same way as when they occur in isolation.</td>

</tr>

<td> </td>

<td valign = "top">(Bi)</td>

<td colspan="2"> In the complex numeral the two constituents are summands.</td>

</tr>

<tr>

<td> </td>

<td valign = "top">(Bii)</td>

<td colspan="2">Complex expressions fall into two parts, a product and a remainder.</td>

</tr>

<tr>

<td> </td>

<td> </td>

<td vallign = "top">(Bii1)</td>

<td>The remainder has the two following properties. It never has a larger value than the next lower base of the total expression.</td>

</tr>

<tr>

<td> </td>

<td> </td>

<td valign = "top">(Bii2)</td>

<td>the remainder is expressed by the same mathematical function as when it occurs in isolation.</td>

</tr>

</table>
 Keywords  numeral
 Domain  word formation
 Type  no genuine implication; rather: provided that
 Status  achronic
 Quality  absolute
 Basis  56 languages mentioned in Greenberg 1978a
 Source  Greenberg 1978a: 280 (#38)

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Discussion
Notes
1. In (French) French, 70 is expressed as “soixante-dix” and not as “septante”. Above 100 there are no such irregularities except that we can never predict at what point a new higher base will appear, or when we will reach L, the limit (cf. #528).2. Some further explanations: (A,B) An example of a simple numeral (a) is “five-hundred”, of a complex numeral (b) is “five-hundred and sixty-six”. (Aii) English “five hundred” conforms to this, but “fifty” does not. Hence the base for predictable expressions cannot be “ten”. (Bii) In English, e.g., “three hundred and seventy-two”, “three hundred” is a product and “seventy-two” is a remainder. (Bii1) In “three hundred and seventy-two”, e.g., the remainder “ seventy-two” has a value 72, which is smaller than the next lower base of the total expression “three hundred seventy-two”, i.e. 100. This does not hold for French “soixante-douze” in which the remainder 12 > 10.(Bii2) “Three hundred and seventy-two”, e.g., the remainder “seventy-two” is expressed in the same way as in the numeral expressions for 72 in isolation both in its mathematical analysis and phonological expression.
Comment
Frans Plank · 3 Aug 2006
1. In (French) French, 70 is expressed as 'soixante-dix' and not as 'septante'. Above 100 there are no such irregularities except that we can never predict at what point a new higher base will appear, or when we will reach L, the limit (cf. <a class="innerLink" href="browse.php?entry_id=528"><img src="../img/entry.gif" border="0">).

2. Some further explanations:
<table class = "textTable">
<tr>
<td valign = "top">(A,B)</td>
<td> An example of a simple numeral (a) is 'five-hundred', of a complex numeral (b) is 'five-hundred and sixty-six'.</td>
</tr>
<td valign = "top">(Aii)</td>
<td>English 'five hundred' conforms to this, but 'fifty' does not. Hence the base for predictable expressions cannot be 'ten'.</td>
</tr>
<tr>
<td valign = "top">(Bii)</td>
<td>In English, e.g.,'three hundred and seventy-two', 'three hundred' is a product and 'seventy-two' is a remainder.</td>
</tr>
<tr>
<td valign = "top">(Bii1)</td>
<td>In 'three hundred and seventy-two', e.g., the remainder 'seventy-two' has a value 72, which is smaller than the next lower base of the total expression 'three hundred seventy-two', i.e. 100. This does not hold for French 'soixante-douze' in which the remainder 12 > 10.</td>
</tr>
<tr>
<td valign = "top">(Bii2)</td>
<td>'Three hundred and seventy-two', e.g., the remainder 'seventy-two' is expressed in the same way as in the numeral expressions for 72 in isolation both in its mathematical analysis and phonological expression.</td>
</tr>
</table>