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diff --git a/2004-en-alt/ithkuil-ch-12-numbers.html b/2004-en-alt/ithkuil-ch-12-numbers.html new file mode 100644 index 0000000..a53bc60 --- /dev/null +++ b/2004-en-alt/ithkuil-ch-12-numbers.html @@ -0,0 +1,557 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> +<!-- saved from url=(0043)ithkuil-ch12-numbers.htm --> +<HTML><HEAD><META http-equiv="Content-Type" content="text/html; charset=ISO-8859-1"> +<TITLE>A Grammar of the Ithkuil Language - Chapter 12: The Number System</TITLE> + +<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="assets/Title-Script5.gif"><BR> + <BR> +</DIV> +<TABLE width="100%" border="0" cellpadding="1"> + <TBODY><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.html" 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.html">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.html">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.html">Introduction</A></FONT></DIV></TD> + <TD valign="top"><DIV align="left"><FONT face="Arial, Helvetica, sans-serif"><A href="ithkuil-ch5b-verbs-contd.html">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.html">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.html">1 + Phonology</A></FONT></DIV></TD> + <TD valign="top"><DIV align="left"><FONT face="Arial, Helvetica, sans-serif"><A href="ithkuil-ch6-moreverbs.html">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.html">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.html">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.html">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="assets/ithkuil-ch-12-numbers.html">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.html">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.html">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.html">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.html">4 + Case Morphology </A></FONT> </TD> + <TD valign="top"><FONT face="Arial, Helvetica, sans-serif"><A href="ithkuil-ch8-adjuncts.html">8 + Adjuncts</A></FONT></TD> + <TD valign="top"><FONT face="Arial, Helvetica, sans-serif"><A href="ilaksh/Ilaksh_Intro.html" target="_blank">Revised Ithkuil: <FONT face="Times New Roman, Times, serif">I</FONT>laksh</A></FONT></TD> + </TR> +</TBODY></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"> + <TBODY><TR> + <TD width="329"><FONT size="2"><A href="ithkuil-ch12-numbers.htm#Sec12o1">12.1 Features of a Centesimal + Number System</A></FONT></TD> + </TR> + <TR> + <TD><FONT size="2"><A href="ithkuil-ch12-numbers.htm#Sec12o2">12.2 Semantic Designations for Numerical + Stems </A></FONT></TD> + </TR> + <TR> + <TD><FONT size="2"><A href="ithkuil-ch12-numbers.htm#Sec12o3">12.3 Expressing “Zero”</A></FONT></TD> + </TR> + <TR> + <TD><FONT size="2"><A href="ithkuil-ch12-numbers.htm#Sec12o4">12.4 Writing Numerals</A></FONT></TD> + </TR> + <TR> + <TD><FONT size="2"><A href="ithkuil-ch12-numbers.htm#Sec12o5">12.5 Using Numbers in Speech</A></FONT></TD> + </TR> + </TBODY></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#Sec4o5o7">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"> + <TBODY><TR> + <TD><P><FONT size="4"><STRONG>12.1 FEATURES OF A CENTESIMAL NUMBER SYSTEM<A name="Sec12o1"></A></STRONG></FONT></P></TD> + </TR> + </TBODY></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="assets/12-1a.gif" width="29" height="16" align="absmiddle"> + (100 million, i.e., 10,000 ten-thousands). The final unit is <IMG src="assets/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="assets/12-1c.gif" width="36" height="15">, + 777 of<FONT color="#FFFFFF">_</FONT><IMG src="assets/12-1d.gif" width="35" height="15">, + 321 of<FONT color="#FFFFFF">_</FONT><IMG src="assets/12-1e.gif" width="36" height="14">, + and 456 of<FONT color="#FFFFFF">_</FONT><IMG src="assets/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="assets/12-1g.gif" width="49" height="18" align="absmiddle">, + 2177 of<FONT color="#FFFFFF">_<IMG src="assets/12-1h.gif" width="48" height="18" align="absmiddle"></FONT>, + and 4563 of<FONT color="#FFFFFF">_<IMG src="assets/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"> + <TBODY><TR> + <TD><P><FONT size="4"><STRONG>12.2 SEMANTIC DESIGNATIONS FOR NUMERICAL STEMS<A name="Sec12o2"></A></STRONG></FONT></P></TD> + </TR> + </TBODY></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="assets/10-1-1c.gif" width="34" height="18" align="absmiddle"> + Affix with Numerals</STRONG></FONT></P> +<P align="justify"><IMG src="assets/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="ithkuil-ch12-numbers.htm#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"> + <TBODY><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="assets/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> +</TBODY></TABLE> +<BR> +<TABLE width="75%" border="1" cellpadding="1"> + <TBODY><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> +</TBODY></TABLE> + +<P> </P> +<TABLE width="99%" border="0" cellpadding="0" bgcolor="#CCCCCC"> + <TBODY><TR> + <TD><P><FONT size="4"><STRONG>12.3 EXPRESSING “ZERO” <A name="Sec12o3"></A></STRONG></FONT></P></TD> + </TR> +</TBODY></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"> + <TBODY><TR> + <TD><P><FONT size="4"><STRONG>12.4 WRITING NUMERALS<A name="Sec12o4"></A></STRONG></FONT></P></TD> + </TR> +</TBODY></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="assets/12-4a.gif" width="23" height="30" align="top">, + while ‘one million’ can be written as <IMG src="assets/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#Sec11o3o2">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="assets/12-4c.gif" width="639" height="621"> <BR> + <IMG src="assets/12-4d.gif" width="639" height="681"><BR> + <BR> + <IMG src="assets/12-4e.gif" width="320" height="135"></P> +<P> </P> +<TABLE width="99%" border="0" cellpadding="0" bgcolor="#CCCCCC"> + <TBODY><TR> + <TD><P><FONT size="4"><STRONG>12.5 USING NUMBERS IN SPEECH<A name="Sec12o5"></A></STRONG></FONT></P></TD> + </TR> +</TBODY></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="assets/12-5a.gif" width="165" height="74"><BR> + literally: “42 (of hundreds) 29”<BR> + <EM><STRONG>4229</STRONG></EM> <BR> +</P> +<P><IMG src="assets/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="Sound_Files/Ch-12-1.mp3">Listen!</A> + </FONT></STRONG><EM><STRONG><FONT size="1" face="Arial, Helvetica, sans-serif"><A href="Sound_Files/Ch-12-1.mp3"><IMG src="assets/Audio_icon.gif" width="19" height="16" border="0" align="absbottom"></A></FONT></STRONG></EM></P> +<P> </P> +<P><IMG src="assets/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="assets/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#Sec4o5o6">Sec. 4.5.6</A>) or + the <FONT size="2">ESSIVE</FONT> case (see <A href="ithkuil-ch4-case.htm#Sec4o6o1">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="assets/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="assets/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#Sec9o4">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="assets/12-5h.gif" width="129" height="51"></FONT></P> +<P align="justify"> </P> +<P> +<TABLE width="100%" border="0" cellpadding="1"> + <TBODY><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.html" 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.html">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.html">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.html">Introduction</A></FONT></DIV></TD> + <TD valign="top"><DIV align="left"><FONT face="Arial, Helvetica, sans-serif"><A href="ithkuil-ch5b-verbs-contd.html">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.html">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.html">1 + Phonology</A></FONT></DIV></TD> + <TD valign="top"><DIV align="left"><FONT face="Arial, Helvetica, sans-serif"><A href="ithkuil-ch6-moreverbs.html">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.html">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.html">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.html">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="assets/ithkuil-ch-12-numbers.html">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.html">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.html">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.html">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.html">4 + Case Morphology </A></FONT> </TD> + <TD valign="top"><FONT face="Arial, Helvetica, sans-serif"><A href="ithkuil-ch8-adjuncts.html">8 + Adjuncts</A></FONT></TD> + <TD valign="top"><FONT face="Arial, Helvetica, sans-serif"><A href="ilaksh/Ilaksh_Intro.html" target="_blank">Revised Ithkuil: <FONT face="Times New Roman, Times, serif">I</FONT>laksh</A></FONT></TD> + </TR> +</TBODY></TABLE> +</P><P><FONT size="-1">©2004-2009 by John Quijada. You may copy or excerpt any portion + of the contents of this website provided you give full attribution to the author + and this website. </FONT></P> +<P> </P> <P></P> + + +</BODY></HTML>
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