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diff --git a/2004-en/ithkuil-ch12-numbers.htm b/2004-en/ithkuil-ch12-numbers.htm new file mode 100644 index 0000000..a83d599 --- /dev/null +++ b/2004-en/ithkuil-ch12-numbers.htm @@ -0,0 +1,558 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> +<html> +<head> +<title>A Grammar of the Ithkuil Language - Chapter 12: The Number System</title> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<script language="JavaScript" type="text/JavaScript"> +<!-- +//-->onLoad="javascript:changenav12();" +</script> +</head> + +<body> +<div align="center"><font color="#999999" face="Verdana, Arial, Helvetica, sans-serif"><strong>Ithkuil: + A Philosophical Design for a Hypothetical Language</strong></font><br> + <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Title-Script5.gif"><br> + <br> +</div> +<table width="100%" border="0" cellpadding="1"> + <tr> + <td width="9%" height="25" valign="top"><div align="left"><font size="1"><a name="menu"></a></font></div></td> + <td width="27%" valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="index.htm" target="_top">Home</a></font></div></td> + <td width="37%" valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch5a-verbs.htm">5a + Verb Morphology </a></font></div></td> + <td width="27%" valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch9-syntax.htm">9 + Syntax</a></font></font></div></td> + </tr> + <tr> + <td height="26" valign="top"><div align="left"><font size="2"><font face="Arial, Helvetica, sans-serif"></font></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-intro.htm">Introduction</a></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch5b-verbs-contd.htm">5b + Verb Morphology (continued)</a></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch10-lexicosemantics.htm">10 + Lexico-Semantics</a></font></div></td> + </tr> + <tr> + <td height="26" valign="top"><div align="left"><font size="2"></font></div></td> + <td valign="top"><div align="left"><font size="2"></font><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch1-phonology.htm">1 + Phonology</a></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch6-moreverbs.htm">6 + More Verb Morphology</a></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch11-script.htm">11 + The Script </a></font></font></div></td> + </tr> + <tr> + <td height="26" valign="top"> </td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch2-morphophonology.htm">2 + Morpho-Phonology</a></font><font size="2"> </font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch7a-affixes.htm">7a + Using Affixes </a></font></font></font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch12-numbers.htm">12 + The Number System</a></font></font></font></td> + </tr> + <tr> + <td height="26" valign="top"> </td> + <td valign="top"><font size="2"> </font><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch3-morphology.htm">3 + Basic Morphology</a></font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch7b-affixes-contd.htm">7b + Using Affixes (continued) </a></font></font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-lexicon.htm">The + Lexicon</a></font></font></td> + </tr> + <tr> + <td height="26" valign="top"> </td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch4-case.htm">4 + Case Morphology </a></font> </td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch8-adjuncts.htm">8 + Adjuncts</a></font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="Ilaksh_Intro.html" target="_blank">Revised Ithkuil: <font face="Times New Roman, Times, serif">I</font>laksh</a></font></td> + </tr> +</table> +<h2 align="center"> </h2> +<h2 align="center">Chapter 12: The Number System</h2> +<div align="center"> + <table width="43%" border="0" cellpadding="1" cellspacing="1"> + <tr> + <td width="329"><font size="2"><a href="#Sec12o1">12.1 Features of a Centesimal + Number System</a></font></td> + </tr> + <tr> + <td><font size="2"><a href="#Sec12o2">12.2 Semantic Designations for Numerical + Stems </a></font></td> + </tr> + <tr> + <td><font size="2"><a href="#Sec12o3">12.3 Expressing “Zero”</a></font></td> + </tr> + <tr> + <td><font size="2"><a href="#Sec12o4">12.4 Writing Numerals</a></font></td> + </tr> + <tr> + <td><font size="2"><a href="#Sec12o5">12.5 Using Numbers in Speech</a></font></td> + </tr> + </table> +</div> +<p align="justify">The Ithkuil system of numbers and counting is distinct from + Western languages in two fundamental ways: it is centesimal (base one hundred) + as opposed to decimal (base ten), and the numbers themselves are full formatives + (i.e., nouns and verbs), not adjectives. This has already been discussed briefly + in <a href="ithkuil-ch4-case.htm">Section 4.5.7</a> regarding + the <font size="2">PARTITIVE</font> case. This section will examine the numerical + system in greater detail.</p> +<p> </p> +<div align="justify"> + <table width="100%" border="0" cellpadding="0" bgcolor="#CCCCCC"> + <tr> + <td><p><font size="4"><strong>12.1 FEATURES OF A CENTESIMAL NUMBER SYSTEM<a name="Sec12o1"></a></strong></font></p></td> + </tr> + </table> +</div> +<p align="justify">Being a centesimal system of enumeration, the numbers from + zero to 100 are considered autonomous units represented by single stems and + written using single autonomous symbols. Beginning with the number 101, numbers + are referred to by the number of hundreds plus the number of units, just as + a decimal system, beginning with the number 11, refers to the number of tens + plus the number of units. However, where a decimal system then shifts to a unit + referring to 100 once “10 tens” is reached, a centesimal system + proceeds to the number 10,000 before establishing a new unit reference (i.e., + “100 hundreds”). Thus the number 3254, which in a decimal system + is 3 thousands — 2 hundreds — 5 tens — 4 ones, in a centesimal + system becomes 32 hundreds—54 ones, and would be only two digits when + written (the single character representing 32, and the single character representing + 54). The details of writing Ithkuil numerals are given below in Section 12.5.</p> +<p align="justify">After 100, separate unit numbers and symbols are assigned to + the square of 100 (i.e. ten thousand, that being “100 hundreds”), + then the square of that number, <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1a.gif" width="29" height="16" align="absmiddle"> + (100 million, i.e., 10,000 ten-thousands). The final unit is <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1b.gif" width="28" height="15" align="baseline">, + that is, 10 quadrillion or 100 million hundred-millions, the last number for + which Ithkuil assigns a separate root and symbol. After ten quadrillion, numbers + are referred to as multiples of lower sets, similar to saying in English “one + trillion quadrillion” instead of the equivalent “one octillion.”</p> +<p align="justify">While the above may seem unwieldy or even arbitrary, it actually + parallels Western base-ten numerals in terms of its systematization. For example, + in a Western number like 456,321,777,123, each set of three numbers between + the commas tells how many hundreds there are of a certain power of 1000 (i.e., + there are 123 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1c.gif" width="36" height="15">, + 777 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1d.gif" width="35" height="15">, + 321 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1e.gif" width="36" height="14">, + and 456 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1f.gif" width="36" height="14">, + or in more common terms 123 ones, 777 thousands, 321 millions, 456 billions).</p> +<p align="justify">The same exact system holds for Ithkuil, except that the sets + of numbers “between the commas” so to speak, is the number of ten-thousands, + not thousands. Thus, if we were to rewrite the Western number 456,321,777,123 + in such a system, it would be <strong>4563,2177,7123</strong> (i.e., 7123 of<font color="#FFFFFF">_</font><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1g.gif" width="49" height="18" align="absmiddle">, + 2177 of<font color="#FFFFFF">_<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1h.gif" width="48" height="18" align="absmiddle"></font>, + and 4563 of<font color="#FFFFFF">_<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-1i.gif" width="49" height="18" align="absmiddle"></font>, + that being 7123 ones, 2177 ten-thousands, and 4563 hundred-millions). </p> + +<p> </p> +<div align="justify"> + <table width="100%" border="0" cellpadding="0" bgcolor="#CCCCCC"> + <tr> + <td><p><font size="4"><strong>12.2 SEMANTIC DESIGNATIONS FOR NUMERICAL STEMS<a name="Sec12o2"></a></strong></font></p></td> + </tr> + </table> +</div> +<p align="justify">The semantic roots for numbers in Ithkuil from 1 to 99 are + based on roots for 1 through 10, to which the nine degrees of the affix <strong>-V<font size="1">1</font>t’</strong> + are added. Each of the nine degrees of this suffix, when applied to one of the + ten number-roots, corresponds to an additional multiple of ten. This is illustrated + in Table 67 below.<br> +</p> +<p align="justify"><font face="Arial, Helvetica, sans-serif"><strong>Table 67: + The <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2010/10-1-1c.gif" width="34" height="18" align="absmiddle"> + Affix with Numerals</strong></font></p> +<p align="justify"><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-2.gif" width="637" height="112"></p> +<p align="justify">The addition of a particular degree of this affix to one of + the ten indicates that the root number is added to that multiple of ten. For + example, the stem <font face="Arial, Helvetica, sans-serif"> <strong>kas</strong></font> + ‘two,’ plus the seventh degree affix <strong>-V1t’/7</strong>, + gives <font face="Arial, Helvetica, sans-serif"><strong>kast’ï</strong></font> + ‘seventy-two.’ Because there is no root corresponding to ‘zero’ + (see <a href="#Sec12o3">Sec. 12.3</a> below), each multiple of ten is constructed using stem <font face="Arial, Helvetica, sans-serif"><strong>mas</strong></font> + ‘ten’ plus one of the above suffixes. Thus, the numbers 20, 30 and + 40 are respectively <strong><font face="Arial, Helvetica, sans-serif">mast’</font></strong>, + <font face="Arial, Helvetica, sans-serif"> <strong>mast’u</strong></font> + and <font face="Arial, Helvetica, sans-serif"><strong>mast’ai</strong></font>, + but the numbers 22, 32 and 42 are <strong><font face="Arial, Helvetica, sans-serif">kast’u</font></strong>, + <strong> <font face="Arial, Helvetica, sans-serif">kast’ai</font></strong> + and <strong><font face="Arial, Helvetica, sans-serif">kast’ei</font></strong>. + This pattern only operates up to the nineties, as there is a separate autonomous + root for 100, <em><font face="Arial, Helvetica, sans-serif"><strong>r-s</strong></font></em>.</p> +<p align="justify">Since numbers are formatives in Ithkuil, not adjectives as + in most Western languages, holistic stem No. 1, shown by the vocalic infix <font face="Arial, Helvetica, sans-serif"><strong>-a-</strong></font>, + is a formative signifying a set containing a number of members corresponding + to that particular root. Thus, the formative <strong><font face="Arial, Helvetica, sans-serif">kas</font></strong> + above, translatable as ‘two,’ actually means ‘a set of two; + a duo / to be a duo.’ In turn, the two complementary derivatives of each + stem denote its multiple and its fraction respectively. This is illustrated + below for both Form I and II using the roots <font face="Arial, Helvetica, sans-serif"><strong>k-s</strong></font>, + <font size="2">TWO</font>, and <font face="Arial, Helvetica, sans-serif"><strong>n-s</strong></font>, + meaning <font size="2">SEVEN</font>:</p> +<p align="justify">For <strong><font face="Arial, Helvetica, sans-serif">k-s</font></strong>, + <font size="2">TWO</font>:</p> +<p>1. <strong><font face="Arial, Helvetica, sans-serif">kas/kâs</font></strong> + <em>‘a set of two, a duo; to be two in number’</em></p> +<blockquote> + <p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br> + <font face="Arial, Helvetica, sans-serif"><strong>kes/kês</strong></font>: + <em>‘twice the number of something; to double, to multiply by two’</em><br> + <strong><font face="Arial, Helvetica, sans-serif">käs/kaes</font></strong>: + <em>‘a half; to halve, to be or make half, to divide by or in two’</em></p> +</blockquote> +<p>2. <strong><font face="Arial, Helvetica, sans-serif">kus/kûs</font></strong> + <em>‘to be or make dual; having two uses or aspects; bi-; twofold’ + </em></p> +<blockquote> + <p><font size="2">COMPLEMENTARY DERIVATIVES</font>:<br> + <font face="Arial, Helvetica, sans-serif"><strong>kos/kôs</strong></font>: + <em>‘two times (i.e., iterations), twice; to be/do/make twice’</em><br> + <strong><font face="Arial, Helvetica, sans-serif">kös/køs</font></strong>: + <em>‘to be of or make into two parts; bifurcate(d)’</em></p> +</blockquote> +<p>3. <font face="Arial, Helvetica, sans-serif"><strong>kis/kîs</strong></font> + <em>‘the second one in a sequence; to be or make second (in a sequence)’</em></p> +<blockquote> + <p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br> + <font face="Arial, Helvetica, sans-serif"><strong>kës/kÿs</strong></font>: + ‘to the second power, squared; to square, raise to the 2nd power<em>’</em><br> + <strong><font face="Arial, Helvetica, sans-serif">küs/kius</font></strong>: + <em>‘to the negative second power, the inverse square; to divide by + the square of’</em></p> +</blockquote> +<p>For <strong><font face="Arial, Helvetica, sans-serif">n-s</font></strong>, + <font size="2">SEVEN</font>:</p> +<p>1. <strong><font face="Arial, Helvetica, sans-serif">nas/nâs</font></strong> + ‘a set/group of seven, a septet; to be seven in number’</p> +<blockquote> + <p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br> + <font face="Arial, Helvetica, sans-serif"><strong>nes/nês</strong></font>: + <em>‘7 times the number of something; to multiply by 7; septuple’</em><br> + <strong><font face="Arial, Helvetica, sans-serif">näs/naes</font></strong>: + <em>‘a seventh; to be or make a 7th part of something, to divide by + 7 or into 7 parts’</em></p> +</blockquote> +<p>2. <font face="Arial, Helvetica, sans-serif"><strong>nus/nûs</strong></font> + ‘to be or make seven-faceted; having 7 uses or aspects; septi-; sevenfold’ +</p> +<blockquote> + <p><font size="2">COMPLEMENTARY DERIVATIVES</font>:<br> + <strong><font face="Arial, Helvetica, sans-serif">nos/nôs</font></strong>: + <em>‘7 times (i.e., iterations); to be/do/make 7 times’</em><br> + <strong><font face="Arial, Helvetica, sans-serif">nös/nøs</font></strong>: + <em>‘to be of or make into 7 parts; separate(d) into 7 parts’</em></p> +</blockquote> +<p>3. <font face="Arial, Helvetica, sans-serif"><strong>nis/nîs</strong></font> + <em>‘the seventh one in a sequence; to be or make 7th (in a sequence)’ + </em> </p> +<blockquote> + <p><font size="2">COMPLEMENTARY DERIVATIVES</font>:<br> + <font face="Arial, Helvetica, sans-serif"><strong>nës/nÿs</strong></font>: + <em>‘to the 7th power; to raise to the 7th power’ </em><br> + <strong><font face="Arial, Helvetica, sans-serif">nüs/nius</font></strong>: + <em>‘to the negative 7th power; to divide by the 7th power of’ + </em> </p> +</blockquote> +<p align="justify">In addition to the above-described roots, there is the root + <font face="Arial, Helvetica, sans-serif"><strong>l-s</strong></font>, <font size="2">ONE/UNITY</font>. + As this root has no multiples, its semantic designations follow a unique pattern. + <font size="2">NOTE</font>: The <font size="2">INFORMAL</font> versus <font size="2">FORMAL</font> + distinction in this root (i.e., Form I versus Form II of each stem) distinguishes + between a focus on non-duplication/singularity for the <font size="2">INFORMAL</font>, + and indivisibility/unity for the <font size="2">FORMAL</font>:</p> +<p> 1. <strong><font face="Arial, Helvetica, sans-serif">las/lâs</font></strong> + <em>‘a single entity; to be one in number’ </em></p> +<blockquote> + <p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br> + <strong><font face="Arial, Helvetica, sans-serif">les/lês</font></strong>: + <em>‘to be indivisible, whole, a single unit; unitary; to unify’</em><br> + <font face="Arial, Helvetica, sans-serif"><strong>läs/laes</strong></font>: + <em>‘to be (an) individual, a distinct entity in itself; to individualize’</em></p> +</blockquote> +<p>2. <strong><font face="Arial, Helvetica, sans-serif">lus/lûs</font></strong> + ‘a lone entity, something alone; an entity in solitude, something/someone + isolated; be alone; to isolate; be in solitude’</p> +<blockquote> + <p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br> + <strong><font face="Arial, Helvetica, sans-serif">los/lôs</font></strong>: + <em>‘something/someone lonely; be or make lonely’</em><br> + <font face="Arial, Helvetica, sans-serif"><strong>lös/løs</strong></font>: + <em>‘something/someone independent, self-sufficient, singular (i.e., + without need of, connection to, or dependency on others); be or make independent, + self-sufficient, singular’</em></p> +</blockquote> +<p>3. <font face="Arial, Helvetica, sans-serif"><strong>lis/lîs</strong></font> + ‘something/someone unique, the only one; to be or make unique’</p> +<blockquote> + <p> <font size="2">COMPLEMENTARY DERIVATIVES</font>:<br> + <strong><font face="Arial, Helvetica, sans-serif">l</font><font face="Arial, Helvetica, sans-serif">ës/lÿs</font></strong>: + <em>‘a sole entity, the only one available or able (in terms of sufficiency + or applicability to the context)’</em><br> + <font face="Arial, Helvetica, sans-serif"><strong>lüs/lius</strong></font>: + <em>‘something/someone one-of-a-kind, unparalleled, without equal or + peer (in terms of uniqueness of characteristics)’</em></p> +</blockquote> +<p><br> + The Ithkuil numerical roots as described in the section above are as follows:</p> +<table width="75%" border="1" cellpadding="1"> + <tr> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">l-s</font></strong></div></td> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">k-s</font></strong></div></td> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">š-s</font></strong></div></td> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">p-s</font></strong></div></td> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif"><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%201/Symbols/t-cedilla.gif" width="7" height="16" align="absbottom">-s</font></strong></div></td> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">t-s</font></strong></div></td> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">n-s</font></strong></div></td> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">x-s</font></strong></div></td> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif"> + f-s</font></strong></div></td> + <td><div align="center"><strong><font face="Arial, Helvetica, sans-serif">m-s</font></strong></div></td> + </tr> + <tr> + <td><div align="center"><em>one</em></div></td> + <td><div align="center"><em>two</em></div></td> + <td><div align="center"><em>three</em></div></td> + <td><div align="center"><em>four</em></div></td> + <td><div align="center"><em>five</em></div></td> + <td><div align="center"><em>six</em></div></td> + <td><div align="center"><em>seven</em></div></td> + <td><div align="center"><em>eight</em></div></td> + <td><div align="center"><em>nine</em></div></td> + <td><div align="center"><em>ten</em></div></td> + </tr> +</table> +<br> +<table width="75%" border="1" cellpadding="1"> + <tr> + <td width="19%"><div align="center"><strong><font face="Arial, Helvetica, sans-serif">r-s</font></strong></div></td> + <td width="22%"><div align="center"><strong><font face="Arial, Helvetica, sans-serif">q-s</font></strong></div></td> + <td width="27%"><div align="center"><strong><font face="Arial, Helvetica, sans-serif">ç-s</font></strong></div></td> + <td width="32%"><div align="center"><strong><font face="Arial, Helvetica, sans-serif">c-s</font></strong></div></td> + </tr> + <tr> + <td><div align="center"><em>one hundred</em></div></td> + <td><div align="center"><em>ten thousand</em></div></td> + <td><div align="center"><em>one hundred million</em></div></td> + <td><div align="center"><em>ten quadrillion</em></div></td> + </tr> +</table> + +<p> </p> +<table width="99%" border="0" cellpadding="0" bgcolor="#CCCCCC"> + <tr> + <td><p><font size="4"><strong>12.3 EXPRESSING “ZERO” <a name="Sec12o3"></a></strong></font></p></td> + </tr> +</table> +<p align="justify"> Ithkuil has no word for “zero” nor is it conceptualized + as a numerical category. Instead any appropriate formative may take the affixes + -V1ss/1 or -V2ss/1 <em>‘no amount of’</em> or -V3b/1 <em>‘no…at + all’</em> in terms of degree or extent to create negative expressions + that convey the idea of an absence of a numerical entity or quantity. In many + cases, simply the negative of whatever formative is under discussion may be + used. </p> +<p align="justify">As for handling the concept of zero as a null placeholder when + writing Ithkuil numbers, this is addressed in Section 12.4 below.</p> + +<p> </p> +<table width="99%" border="0" cellpadding="0" bgcolor="#CCCCCC"> + <tr> + <td><p><font size="4"><strong>12.4 WRITING NUMERALS<a name="Sec12o4"></a></strong></font></p></td> + </tr> +</table> +<p align="justify">Writing Ithkuil numerals is somewhat similar to writing numbers + in Western languages (i.e., “Arabic” numerals), in that the interpretation + of a number as a different power of 100 (analogous to interpreting single Arabic + numerals as either ones, tens, hundreds, thousands, etc.) is based on its sequence + within the entire number. However, there are two aspects of writing Ithkuil + numbers that are quite different from Arabic numbers.:</p> +<ol> + <li> + <div align="justify">Ithkuil does not employ a symbol for zero. Instead, Ithkuil + employs separate autonomous symbols for each power of 100 (100, 10,000, + 100 million, etc.) each of which operates as the appropriate placeholder + instead of zero. To illustrate what this means by analogy, pretend that + “@” is an autonomous symbol for 27 (since Ithkuil numbers from + 1 to 99 each have a separate symbol), “&” is a symbol for + 100, “#” is a symbol for 10,000 and there is no symbol 0 (zero). + The numbers 2700, 2705, 327, 22700 and 4,270,027 would then be written @&, + @5, 3@, 2@&, and 4@#@ respectively. (NOTE: In actual practice, numbers + which contain the “hundred” symbol, here represented as “&,” + normally place a dot above or below the adjacent numeral and dispense with + the &, indicating that the number so marked is to be multiplied by 100. + Thus, 2@& would actually be written as <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4a.gif" width="23" height="30" align="top">, + while ‘one million’ can be written as <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4b.gif" width="9" height="26" align="top"> + instead of writing &#.<br> + </div> + </li> + <li> + <div align="justify">Since Ithkuil is a base-100 system, numbers do not become + two digits in length until the hundreds, do not become three digits in length + until the ten thousands, do not become four digits in length until the millions, + etc.</div> + </li> +</ol> +<p align="justify"> </p> +<p align="justify">One must also remember that in terms of left-to-right or up-and-down + orientation, numbers follow the <em>boustrophedon</em> mode the same as the + Ithkuil script (see <a href="ithkuil-ch11-script.htm">Sec. 11.3.2</a>). + Similarly to Western languages, small non-compound numbers can be written using + either their numerical symbols or written out in script (as in English “12” + versus “twelve”).</p> +<p align="justify">The following table gives the Ithkuil numerical symbols along + with their morphological stems:<br> + <br> + <font face="Arial, Helvetica, sans-serif"><strong>Table 68: ITHKUIL NUMERICAL + STEMS AND WRITTEN SYMBOLS</strong></font><br> + <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4c.gif" width="639" height="621"> <br> + <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4d.gif" width="639" height="681"><br> + <br> + <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-4e.gif" width="320" height="135"></p> +<p> </p> +<table width="99%" border="0" cellpadding="0" bgcolor="#CCCCCC"> + <tr> + <td><p><font size="4"><strong>12.5 USING NUMBERS IN SPEECH<a name="Sec12o5"></a></strong></font></p></td> + </tr> +</table> +<p align="justify">Spoken numbers are formed from the above stems using both the + <font size="2">PARTITIVE</font> and <font size="2">COMITATIVE</font> cases, + as well as using the coordinative affix <strong>-V<font size="1">1</font>w/1</strong> + (= <strong><font face="Arial, Helvetica, sans-serif">-iw</font></strong> or + <font face="Arial, Helvetica, sans-serif"><strong>-wai</strong></font>). The + number of largest base units is shown by placing the base-unit term in the <font size="2">PARTITIVE</font>. + If this is then followed by another collection of smaller base units, that number + of smaller base units is connected using the <font size="2">COMITATIVE</font> + case while the smaller base-unit term is again in the <font size="2">PARTITIVE</font>. + Single units (from 1 to 99) are connected by the coordinative affix when they + are part of the number of hundreds or higher base-units. </p> +<p align="justify">It should be noted that when pronouncing numbers greater than + 199, it is normal in Ithkuil to omit the word <font face="Arial, Helvetica, sans-serif"><strong><em>ra’wirs</em></strong></font> + (= the <font size="2">PARTITIVE</font> of <strong><font face="Arial, Helvetica, sans-serif">ras</font></strong> + ‘one hundred’) referring to the number of hundreds. This is equivalent + to the custom in colloquial English of saying ‘three twelve’ for + ‘three hundred (and) twelve.’ The difference is that in Ithkuil, + this omission of the word for ‘hundred’ is the preferred option, + the word <em>ra’wirs</em> being used only in larger numbers for clarity’s + sake.</p> +<p align="justify">These principles are illustrated by the following examples:</p> +<p><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5a.gif" width="165" height="74"><br> + literally: “42 (of hundreds) 29”<br> + <em><strong>4229</strong></em> <br> +</p> +<p><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5b.gif" width="285" height="75"><br> + literally: “26 of ten-thousands with 97 (of hundreds) 66” = 26,9766<font color="#FFFFFF"></font><br> + <em><strong>269,766<br> + </strong></em><strong><font size="1" face="Arial, Helvetica, sans-serif"><a href="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Sound_Files/Ch-12-1.mp3">Listen!</a> + </font></strong><em><strong><font size="1" face="Arial, Helvetica, sans-serif"><a href="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Sound_Files/Ch-12-1.mp3"><img src="Audio_icon.gif" width="19" height="16" border="0" align="absbottom"></a></font></strong></em></p> +<p> </p> +<p><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5c.gif" width="159" height="73"><br> + literally: “21 of hundred of ten-thousands”<br> + <strong><em>21,000,000</em></strong> <br> + [NOTE: <em>ra’wirs</em> is required in this example]</p> +<p><br> + <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5d.gif" width="651" height="72"><br> + literally: <br> + “72 of hundreds and 79 of hundred-millions with 3 of hundreds and 53 of + ten-thousands with 34 of hundreds 60” <br> + <strong>727,903,533,460</strong></p> +<p align="justify"><br> + We have already seen that when numbers are used to indicate how many of a certain + noun there are, the noun must appear in the <font size="2">PARTITIVE</font> + case, since the number itself is functioning as the “head” of the + numerical expression (e.g., English “12 boxes” being constructed + in Ithkuil as a “12-set of a box” or perhaps more appropriately + a “box-dozen”). Another syntactical consequences of numbers being + full formatives is when a number functions as a label or overt identifier, as + in the English sentence <em>You’ll find him in Room 216.</em> Such usage + of numbers is not primarily sequential (which would involve the equivalent of + “ordinal” numbers such as ‘fourth,’ ‘twenty-sixth’, + etc. equivalent to stem No. 3 of each number root) but rather organizational + (e.g., as in the three-dimensional array of room numbers in a hotel). Ithkuil + handles such organizational labeling using either the <font size="2">CONTRASTIVE</font> + case (see <a href="ithkuil-ch4-case.htm">Sec. 4.5.6</a>) or + the <font size="2">ESSIVE</font> case (see <a href="ithkuil-ch4-case.htm">Sec. + 4.6.1</a>) depending respectively on whether the enumeration of the noun in + question is to distinguish it from other enumerated nouns versus merely identifying + the noun by a numerical name. Examples:</p> +<p><br> + <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5e.gif" width="124" height="63"> <br> + <em>‘the room marked “12”’ </em><font size="2"><strong>OR</strong></font><em> + ‘Room 12’ </em><font size="2"><strong>OR</strong></font><em> ‘Room + No. 12’</em> [i.e., as distinguished from the other numbered rooms]</p> +<p><br> + <img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5f.gif" width="126" height="61"> <br> + <em>‘the room marked “12”’ </em><font size="2"><strong>OR</strong></font><em> + ‘Room 12’ </em><font size="2"><strong>OR</strong></font><em> ‘Room + No. 12’</em> [identifying reference only]</p> +<p align="justify"><br> + Lastly, when numbers comprising multiple number-stems are declined for case, + configuration, extension, etc., rather than writing out the entire number “long-hand,” + the number symbol is used, preceded by the carrier stem <em><strong>kir</strong></em> + (see <a href="ithkuil-ch9-syntax.htm">Sec. 9.4</a>) which carries the appropriate + declensions. This use of the carrier stem applies even to single-stemmed numbers + when writing, in order to allow use of the number symbol instead of writing + it out. In such cases involving single-stemmed numbers, the carrier stem is + not pronounced (rather, the numerical stem bears the pronounced declensions); + it is there only as a written indicator of the declensions to be applied to + the number stem. Thus, the above two examples could also be written as: </p> +<p></p> +<p><img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5g.gif" width="135" height="47"> <font color="#FFFFFF">_________________<img src="https://web.archive.org/web/20090608003714id_/http:/www.ithkuil.net/Images/Ch%2012/12-5h.gif" width="129" height="51"></font></p> +<p align="justify"> </p> +<p> +<table width="100%" border="0" cellpadding="1"> + <tr> + <td width="9%" height="25" valign="top"><div align="left"><font size="1"><a name="menu"></a></font></div></td> + <td width="27%" valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="index.htm" target="_top">Home</a></font></div></td> + <td width="37%" valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch5a-verbs.htm">5a + Verb Morphology </a></font></div></td> + <td width="27%" valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch9-syntax.htm">9 + Syntax</a></font></font></div></td> + </tr> + <tr> + <td height="26" valign="top"><div align="left"><font size="2"><font face="Arial, Helvetica, sans-serif"></font></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-intro.htm">Introduction</a></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch5b-verbs-contd.htm">5b + Verb Morphology (continued)</a></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch10-lexicosemantics.htm">10 + Lexico-Semantics</a></font></div></td> + </tr> + <tr> + <td height="26" valign="top"><div align="left"><font size="2"></font></div></td> + <td valign="top"><div align="left"><font size="2"></font><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch1-phonology.htm">1 + Phonology</a></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch6-moreverbs.htm">6 + More Verb Morphology</a></font></div></td> + <td valign="top"><div align="left"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch11-script.htm">11 + The Script </a></font></font></div></td> + </tr> + <tr> + <td height="26" valign="top"> </td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch2-morphophonology.htm">2 + Morpho-Phonology</a></font><font size="2"> </font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch7a-affixes.htm">7a + Using Affixes </a></font></font></font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch12-numbers.htm">12 + The Number System</a></font></font></font></td> + </tr> + <tr> + <td height="26" valign="top"> </td> + <td valign="top"><font size="2"> </font><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch3-morphology.htm">3 + Basic Morphology</a></font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch7b-affixes-contd.htm">7b + Using Affixes (continued) </a></font></font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-lexicon.htm">The + Lexicon</a></font></font></td> + </tr> + <tr> + <td height="26" valign="top"> </td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch4-case.htm">4 + Case Morphology </a></font> </td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="ithkuil-ch8-adjuncts.htm">8 + Adjuncts</a></font></td> + <td valign="top"><font face="Arial, Helvetica, sans-serif"><a href="Ilaksh_Intro.html" target="_blank">Revised Ithkuil: <font face="Times New Roman, Times, serif">I</font>laksh</a></font></td> + </tr> +</table> +<p><font size="-1">©2004-2009 by John Quijada. 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