From d2da853b9eb430679e7238b93996f8e4651a39c1 Mon Sep 17 00:00:00 2001 From: uakci Date: Sat, 19 Dec 2020 04:55:30 +0100 Subject: fixed encoding --- 2004-en-alt/ithkuil-ch-12-numbers.html | 244 ++++++++++++++++----------------- 1 file changed, 122 insertions(+), 122 deletions(-) mode change 100755 => 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 old mode 100755 new mode 100644 index a53bc60..441719a --- a/2004-en-alt/ithkuil-ch-12-numbers.html +++ b/2004-en-alt/ithkuil-ch-12-numbers.html @@ -79,7 +79,7 @@ Stems - 12.3 Expressing “Zero” + 12.3 Expressing “Zero” 12.4 Writing Numerals @@ -110,21 +110,21 @@ 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 + 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 + “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”), + 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.”

+ 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 @@ -135,7 +135,7 @@ 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, + 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_, @@ -151,7 +151,7 @@

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’ + 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.
@@ -163,91 +163,91 @@

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’ + ‘two,’ plus the seventh degree affix -V1t’/7, + gives kast’ď + ‘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. + ‘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 + 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’

+

1. kas/kñs + ‘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’

+ kes/kęs: + ‘twice the number of something; to double, to multiply by two’
+ kĂ€s/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’ +

2. kus/kƱs + ‘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/kűs: - ‘to be of or make into two parts; bifurcate(d)’

+ kos/kîs: + ‘two times (i.e., iterations), twice; to be/do/make twice’
+ kös/kƙs: + ‘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)’

+

3. kis/küs + ‘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’

+ kĂ«s/k˙s: + ‘to the second power, squared; to square, raise to the 2nd power’
+ kĂŒs/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’

+

1. nas/nñs + ‘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’

+ nes/nęs: + ‘7 times the number of something; to multiply by 7; septuple’
+ nĂ€s/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’ +

2. nus/nƱs + ‘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/nűs: - ‘to be of or make into 7 parts; separate(d) into 7 parts’

+ nos/nîs: + ‘7 times (i.e., iterations); to be/do/make 7 times’
+ nös/nƙs: + ‘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)’ +

3. nis/nüs + ‘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’ + nĂ«s/n˙s: + ‘to the 7th power; to raise to the 7th power’
+ nĂŒs/nius: + ‘to the negative 7th power; to divide by the 7th power of’

In addition to the above-described roots, there is the root @@ -257,37 +257,37 @@ 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’

+

1. las/lñs + ‘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’

+ les/lęs: + ‘to be indivisible, whole, a single unit; unitary; to unify’
+ lĂ€s/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’

+

2. lus/lƱs + ‘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/lűs: - ‘something/someone independent, self-sufficient, singular (i.e., + los/lĂŽs: + ‘something/someone lonely; be or make lonely’
+ lös/lƙs: + ‘something/someone independent, self-sufficient, singular (i.e., without need of, connection to, or dependency on others); be or make independent, - self-sufficient, singular’

+ self-sufficient, singular’

-

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

+

3. lis/lüs + ‘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)’

+ lĂ«s/l˙s: + ‘a sole entity, the only one available or able (in terms of sufficiency + or applicability to the context)’
+ lĂŒs/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:

@@ -295,7 +295,7 @@
l-s
k-s
-
š-s
+
ĆĄ-s
p-s
-s
t-s
@@ -323,7 +323,7 @@
r-s
q-s
-
ç-s
+
ç-s
c-s
@@ -337,13 +337,13 @@

 

- +

12.3 EXPRESSING “ZERO”

12.3 EXPRESSING “ZERO”

-

Ithkuil has no word for “zero” nor is it conceptualized +

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 + -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.

@@ -357,7 +357,7 @@

Writing Ithkuil numerals is somewhat similar to writing numbers - in Western languages (i.e., “Arabic” numerals), in that the interpretation + 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 @@ -368,16 +368,16 @@ 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). + “@” 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 “&,” + 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 + while ‘one million’ can be written as instead of writing &#.
@@ -393,8 +393,8 @@ 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”).

+ 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:

@@ -422,46 +422,46 @@ 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 + 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 + ‘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”
+ literally: “42 (of hundreds) 29”
4229


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


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

+ [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”
+ “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 + 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 + 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’, + “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 @@ -472,17 +472,17 @@ 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’ [i.e., as distinguished from the other numbered rooms]



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

+ ‘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,” + 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 @@ -548,7 +548,7 @@ Revised Ithkuil: Ilaksh -

©2004-2009 by John Quijada. You may copy or excerpt any portion +

©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.

 

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