A Grammar of the Ithkuil Language - Chapter 12: The Number System

From ddbbfedf15e970c02e128294890adbeb97c4a5ae Mon Sep 17 00:00:00 2001 From: uakci Date: Tue, 15 Mar 2022 19:13:44 +0100 Subject: init --- 2004-en-alt/ithkuil-ch-12-numbers.html | 557 +++++++++++++++++++++++++++++++++ 1 file changed, 557 insertions(+) create mode 100644 2004-en-alt/ithkuil-ch-12-numbers.html (limited to '2004-en-alt/ithkuil-ch-12-numbers.html') 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 @@ + + + +A Grammar of the Ithkuil Language - Chapter 12: The Number System + + + +

Ithkuil: + A Philosophical Design for a Hypothetical Language
+

+
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Home	5a + Verb Morphology	9 + Syntax
Introduction	5b + Verb Morphology (continued)	10 + Lexico-Semantics
1 + Phonology	6 + More Verb Morphology	11 + The Script
2 + Morpho-Phonology	7a + Using Affixes	12 + The Number System
3 + Basic Morphology	7b + Using Affixes (continued)	The + Lexicon
4 + Case Morphology	8 + Adjuncts	Revised Ithkuil: Ilaksh

Chapter 12: The Number System

+ + + + + + + + + + + + + + + + +

12.1 Features of a Centesimal + Number System

12.2 Semantic Designations for Numerical + Stems

12.3 Expressing “Zero”

12.4 Writing Numerals

12.5 Using Numbers in Speech

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 Section 4.5.7 regarding + the PARTITIVE case. This section will examine the numerical + system in greater detail.

+ + + + +

12.1 FEATURES OF A CENTESIMAL NUMBER SYSTEM

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.

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, + (100 million, i.e., 10,000 ten-thousands). The final unit is , + 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.”

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_, + 777 of_, + 321 of_, + and 456 of_, + or in more common terms 123 ones, 777 thousands, 321 millions, 456 billions).

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 4563,2177,7123 (i.e., 7123 of_, + 2177 of_, + and 4563 of_, + that being 7123 ones, 2177 ten-thousands, and 4563 hundred-millions).

+ +

+ + + + +

12.2 SEMANTIC DESIGNATIONS FOR NUMERICAL STEMS

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 -V1t’ + 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.
+

Table 67: + The + Affix with Numerals

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 kas + ‘two,’ plus the seventh degree affix -V1t’/7, + gives kast’ï + ‘seventy-two.’ Because there is no root corresponding to ‘zero’ + (see Sec. 12.3 below), each multiple of ten is constructed using stem mas + ‘ten’ plus one of the above suffixes. Thus, the numbers 20, 30 and + 40 are respectively mast’, + mast’u + and mast’ai, + but the numbers 22, 32 and 42 are kast’u, + kast’ai + and kast’ei. + This pattern only operates up to the nineties, as there is a separate autonomous + root for 100, r-s.

Since numbers are formatives in Ithkuil, not adjectives as + in most Western languages, holistic stem No. 1, shown by the vocalic infix -a-, + is a formative signifying a set containing a number of members corresponding + to that particular root. Thus, the formative kas + 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 k-s, + TWO, and n-s, + meaning SEVEN:

For k-s, + TWO:

1. kas/kâs + ‘a set of two, a duo; to be two in number’

+
COMPLEMENTARY DERIVATIVES:
+ kes/kês: + ‘twice the number of something; to double, to multiply by two’
+ käs/kaes: + ‘a half; to halve, to be or make half, to divide by or in two’
+

2. kus/kûs + ‘to be or make dual; having two uses or aspects; bi-; twofold’ +

+
COMPLEMENTARY DERIVATIVES:
+ kos/kôs: + ‘two times (i.e., iterations), twice; to be/do/make twice’
+ kös/køs: + ‘to be of or make into two parts; bifurcate(d)’
+

3. kis/kîs + ‘the second one in a sequence; to be or make second (in a sequence)’

+
COMPLEMENTARY DERIVATIVES:
+ kës/kÿs: + ‘to the second power, squared; to square, raise to the 2nd power’
+ küs/kius: + ‘to the negative second power, the inverse square; to divide by + the square of’
+

For n-s, + SEVEN:

1. nas/nâs + ‘a set/group of seven, a septet; to be seven in number’

+
COMPLEMENTARY DERIVATIVES:
+ nes/nês: + ‘7 times the number of something; to multiply by 7; septuple’
+ näs/naes: + ‘a seventh; to be or make a 7th part of something, to divide by + 7 or into 7 parts’
+

2. nus/nûs + ‘to be or make seven-faceted; having 7 uses or aspects; septi-; sevenfold’ +

+
COMPLEMENTARY DERIVATIVES:
+ nos/nôs: + ‘7 times (i.e., iterations); to be/do/make 7 times’
+ nös/nøs: + ‘to be of or make into 7 parts; separate(d) into 7 parts’
+

3. nis/nîs + ‘the seventh one in a sequence; to be or make 7th (in a sequence)’ +

+
COMPLEMENTARY DERIVATIVES:
+ nës/nÿs: + ‘to the 7th power; to raise to the 7th power’
+ nüs/nius: + ‘to the negative 7th power; to divide by the 7th power of’ +
+

In addition to the above-described roots, there is the root + l-s, ONE/UNITY. + As this root has no multiples, its semantic designations follow a unique pattern. + NOTE: The INFORMAL versus FORMAL + distinction in this root (i.e., Form I versus Form II of each stem) distinguishes + between a focus on non-duplication/singularity for the INFORMAL, + and indivisibility/unity for the FORMAL:

1. las/lâs + ‘a single entity; to be one in number’

+
COMPLEMENTARY DERIVATIVES:
+ les/lês: + ‘to be indivisible, whole, a single unit; unitary; to unify’
+ läs/laes: + ‘to be (an) individual, a distinct entity in itself; to individualize’
+

2. lus/lûs + ‘a lone entity, something alone; an entity in solitude, something/someone + isolated; be alone; to isolate; be in solitude’

+
COMPLEMENTARY DERIVATIVES:
+ los/lôs: + ‘something/someone lonely; be or make lonely’
+ lös/løs: + ‘something/someone independent, self-sufficient, singular (i.e., + without need of, connection to, or dependency on others); be or make independent, + self-sufficient, singular’
+

3. lis/lîs + ‘something/someone unique, the only one; to be or make unique’

+
COMPLEMENTARY DERIVATIVES:
+ lës/lÿs: + ‘a sole entity, the only one available or able (in terms of sufficiency + or applicability to the context)’
+ lüs/lius: + ‘something/someone one-of-a-kind, unparalleled, without equal or + peer (in terms of uniqueness of characteristics)’
+

+ The Ithkuil numerical roots as described in the section above are as follows:

+ + + + + + + + + + + + + + + + + + + + + + + + + +

l-s	k-s	š-s	p-s	-s	t-s	n-s	x-s	+ f-s	m-s
one	two	three	four	five	six	seven	eight	nine	ten

+
+ + + + + + + + + + + + + +

r-s	q-s	ç-s	c-s
one hundred	ten thousand	one hundred million	ten quadrillion

+ +

+ + + + +

12.3 EXPRESSING “ZERO”

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 ‘no amount of’ or -V3b/1 ‘no…at + all’ 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.

As for handling the concept of zero as a null placeholder when + writing Ithkuil numbers, this is addressed in Section 12.4 below.

+ +

+ + + + +

12.4 WRITING NUMERALS

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.:

+
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 , + while ‘one million’ can be written as + instead of writing &#.
+
+
+
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.
+

One must also remember that in terms of left-to-right or up-and-down + orientation, numbers follow the boustrophedon mode the same as the + Ithkuil script (see Sec. 11.3.2). + 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”).

The following table gives the Ithkuil numerical symbols along + with their morphological stems:
+
+ Table 68: ITHKUIL NUMERICAL + STEMS AND WRITTEN SYMBOLS
+
+
+
+

+ + + + +

12.5 USING NUMBERS IN SPEECH

Spoken numbers are formed from the above stems using both the + PARTITIVE and COMITATIVE cases, + as well as using the coordinative affix -V1w/1 + (= -iw or + -wai). The + number of largest base units is shown by placing the base-unit term in the PARTITIVE. + If this is then followed by another collection of smaller base units, that number + of smaller base units is connected using the COMITATIVE + case while the smaller base-unit term is again in the PARTITIVE. + 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.

It should be noted that when pronouncing numbers greater than + 199, it is normal in Ithkuil to omit the word ra’wirs + (= the PARTITIVE of ras + ‘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 ra’wirs being used only in larger numbers for clarity’s + sake.

These principles are illustrated by the following examples:

+ literally: “42 (of hundreds) 29”
+ 4229
+

+ literally: “26 of ten-thousands with 97 (of hundreds) 66” = 26,9766
+ 269,766
+ Listen! +

+ literally: “21 of hundred of ten-thousands”
+ 21,000,000
+ [NOTE: ra’wirs is required in this example]

+
+ literally:
+ “72 of hundreds and 79 of hundred-millions with 3 of hundreds and 53 of + ten-thousands with 34 of hundreds 60”
+ 727,903,533,460

+ 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 PARTITIVE + 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 You’ll find him in Room 216. 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 CONTRASTIVE + case (see Sec. 4.5.6) or + the ESSIVE case (see Sec. + 4.6.1) 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:

+
+ ‘the room marked “12”’ OR + ‘Room 12’ OR ‘Room + No. 12’ [i.e., as distinguished from the other numbered rooms]

+
+ ‘the room marked “12”’ OR + ‘Room 12’ OR ‘Room + No. 12’ [identifying reference only]

+ 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 kir + (see Sec. 9.4) 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:

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Home
5a + Verb Morphology
9 + Syntax
Introduction
5b + Verb Morphology (continued)
10 + Lexico-Semantics
1 + Phonology
6 + More Verb Morphology
11 + The Script
2 + Morpho-Phonology 7a + Using Affixes 12 + The Number System
3 + Basic Morphology 7b + Using Affixes (continued) The + Lexicon
4 + Case Morphology 8 + Adjuncts Revised Ithkuil: Ilaksh
+

+ + + \ No newline at end of file -- cgit v1.2.3