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Further Topics in Vogu II

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Elective Suffixes

Vogu word-formation uses roots and affixes to build words. Since one is generally not at liberty to create ad-hoc words whenever desired, most of the processes of word-formation do not concern the student, but one class of word-forming suffix is freely and frequently used.

These are the elective suffixes, which may be added to any noun in a manner similar to a dependent adjective, but which make a more fundamental change in the meaning of the affixed word. The most common are

These suffixes may be added to a word whenever they apply: sensetltat 'the former teacher'; poSire 'the future king'. The normal rules of crasis apply, but they may not be used independently. The suffix -ton is especially common, serving both as an affectionate dimunitive for persons ( ruDiton 'Little Ruthi') and as a designation of the young of most animals ( abweton 'puppy').

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Nationalities

To indicate individuals of a given nationality, one of the gender prefixes a-, po- or mi- is added to the name stem (usually, the name the national group has given to itself, suitably Vogu-ized): podane, misaambu, adoiC, pomerika 'Kadane man, Saambu woman, German person(s), American man.'

The collective term for nationalities is the name stem plus the collective prefix ka-: kadane, kasaambu, kadoiC, kamerika 'the Kadane/Saambu/German/American people.'

To designate the territory inhabited by a national group, add the suffix -na to the name stem: kadanena, saambuna, doiCna, merikana (kadane is irregular and does not drop the collective ka-). This should not be confused with whatever the official name of a territory may be; instead, this is an informal name, meaning something like 'land of the ...'

The language spoken by a national group is formed from the word fragment vog(u) plus the name stem: vogukadane, vogusaambu, vogudoiC, voguNlIS 'Vogu, Saambu language, German, English.'

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Transitive and Intransitive Verbs

Transitive verbs are those which apply their action to an object; intransitive verbs apply to action to the subject, perhaps onself. Many verbs in Vogu can be transitive or intransitive at will (so long as the meaning applies), eg. ZaCDa 'to burn'. Others, however, have separate forms for transitive and intransitive, eg.: bIkonC 'to stop (smthg)' and IkonC 'to stop'; Deva 'to break (smthg)' and braka 'to break'. Others exist only in the transitive (myot 'to wash (sbdy/smthg)') or intransitive (dvig 'to move'). There is no way to tell from the form of the verb which type it is; it must be learned from the dictionary.

If one requires an intransitive form of a definately transitive verb, there are two stragegies one can use:

The causative mode can render intransitives as transitive: udvig Cidi 'The car moves'; usredvig ani Cido 'I move the car'. Predicate adjectives are always intransitive, and require the causative to function transitively: ukuwi Daskritl 'The dress is dry'; usrekuwi ani Daskritlo 'I dry the dress.'

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Complex Sentences and Conjunctions

Complex sentences are made up of two or more verb phrases. Syntactically, they are of two types: dependent and independent. Morphologically, there are three types: relative, conjunctive and gerundive.

Relative

A relative clause generally modifies a noun or noun phrase, and acts as a verb phrase supplying supplimental information about the noun. These can be formed from participles, which take the noun complement of the antecedant. As a verbal form, the participle can take objects and other complements: uvId ani povka pohalat Dabmaga 'I see a man reading a book.' Relatives can also be formed from the adjective -gUd. This adjective is always used independently, with the noun complement proper to its antecedant. It occupies the same position and takes the same postpositions in the relative phase that the antecedant would occupy in an independent sentence: uvId ani povka, Redar Du Dabmaga pogdi 'I see the man to whom you gave the book.'

Relative adverbs are postpositional adverbial phrases formed with -gUd (often in the varient -gud). They have the same form of antecedant-relative as the adjectival relative, except that the antecedant must be the same type of postpositonal adverb: kvrenkri pul, kavgukri ulekr Du 'Come when you want to (lit. 'come at the time, at which time you want').

Conjunctive

Conjunctive sentences contain two or more verb phrases. In some cases, each verb phrase is a complete thought in its own right, and they are united by a conjunction. In other cases, only one verb phrase is considered the main phrase, and any other phrases in the sentence are subordinate to it.

Independent verb phrases are united by conjunctions. Conjunctions are particles which serve to relate the independent phrases to each other. Vogu grammarians distinguish connective conjunctions, which unite two verb phrases on an equal basis, and correlative conjunctions, in which one of the verb phrases relates to the other in some way.

The connective conjunctions are (note that some have short forms):

ebIr/e
'and (in general, or grouping)'
myoso
'and (simultaneously)'
kaRi
'and, next, then (succession of events)'
Qebe/Qe
'or'
ina/na
'but (contrastive)'
dojo
'and, but, whereas, while'

dojo is midway between ebIr and ina on a spectrum of contrasts. It implies a contrast between the verb phrases, but not so absolute as ina.

The correlative conjunctions are found in pairs, one for each phrase, indicating the way in which they relate to each other. The most common are:

es...go
'if...then' (when the 'if' verb is in the concessive tense)
'when...then' (when the 'if' verb is non-concessive)
es natko...go nole
'as...so'
esduku...go
'Inasmuch as...therefore'
es...myoN
'although...nevertheless'
ebIr...ebIr
'both...and'
Qebe...Qebe
'either...or'
jiman...myoN
'even though/even if...nevertheless'
traZ...domyo
'far from/instead of...rather'

Subordinate verb clauses are formed from postpositions plus verb phrases. Those subordinate clauses that act like adverbs to modify the entire main verb phrase (normally to show the time relationship between the two) are formed from the o-verb gerundive form plus appropriate postposition. Other clauses are the object (or some other complement) of the main verb. The usual way of expressing these is through a nat-, bUn construction (with appropriate postposition on nat-) and a complete verbal phrase. Some common idioms using nat-, bUn are:

nata, bUn
'that' (direct object of the main verb)
natrata, bUn
'in order to, in order that, so that'
natrenaS, bUn
'despite the fact that'
natetl, bUn
'in accordance with the fact that'
natbINo, bUn
'as if, like'
naduku, bUn
'because of, since (as a consequence)'
natija, bUn
'although, contrary to the fact that'
natnu, bUn
'besides, in addition to the fact that'
nateta, bUn
'so long as, provided that'
naQoS, bUn
'unless, except that'
natflaka, bUn
'as a consequence of the fact that, as a result of'
naDCem, bUn
'than'

Gerundive

Gerundive verb phrases are those formed from the infinitive form of the verb. They generally express the temporal relationship between the main verb and subordinate clause. The infinitive is made by addition of the verb prefix o- to the verb stem; the prefix does not affect the accent or cause loss of fleeting vowel in the verb stem. The logical subject of the o-verb phrase takes the postposition -av, and any other nouns take their usual postpositions. The verb itself also takes a postposition to indicate its time relationship. This is often called a conjunctive postposition by Vogu grammarians, particularly because some have different meanings than when used with a simple noun. The most common are:

-ki
'since' (time since an event, not 'whereas')
-Sa
'after'
-bla
'before'
-iS
'until'
-eta
'with, while' (simultaneity; events begin at the same time, but may have different durations)
-kri
'while, during' (duration; events co-occur, i.e, have the same starting and ending points)
-ank
'not, without'(normal way of negating a subordinate postpositional phrase; -ak is not used)
Mention should be made of the other uses of the gerundive form, as a nominative subject or object of certain verbs: nasbri uZnak opoluber 'Fishing is not allowed here'; urzra ani olata 'I know how to read.'

We should also note that there is a certain amount of overlap between the two forms of subordinate clauses. In particular, the o-verb form will often be used in colloquial speech in place of a nat-, bUn phrase: odareta Duv kapleSta, upleSt ani = upleSt ani nateta, bUn udar Du kapleSta 'I will eat so long as you give food.' Keep in mind, however, that the o-verb form is more limited than the nat-, bUn form, since tense or mode affixes are not used with it.

The reverse usage, however, is not common. nat-, bUn phrases are never used in speech with temporal postpositions. Even in writing, the o-verb forms are used for temporal relationships, except in the highest registers of formal exposition. Used anywhere else, a phrase like ugu Du naDkri, bUn upleSt 'You talk while you eat' would seem exceedingly pompous.

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Using Grammatical Particles

Grammatical particles are independent words that modify a sentence or verb phrase. They differ from adverbial particles only in that their action on the phrase is more extensive than an adverb, modifying the meaning in a fundamental way that would require a major change in phrasing in English. Most of these particles modify verbs and stand immediately after them, but others modify phrases or even nouns. The most common grammatical particles of Vogu are
byu
With the concessive tense, this particle is used to translate 'would' (that is, conditional willingness). It is often paired with es...go. Since the concessive exists only in the present, a periphrastic formation is used for other tenses: es dalat Du, go daLiS byu ani 'If you should read, I would listen'; es Relat Du, go da byu, bUn ReLiS ani 'If you had read, I would have listened.'
cUmo
This particle plus a verb in the future tense indicates intention: palat cUmo ani 'I intend to read'.
dyemi
Indicates possibility. It can be used with any tense of the verb: ulat dyemi ani 'I might read'. The particle itself carries a future meaning, so the verb can remain in the present even if referring to a future event. When the future tense is used, it implies that the possibility is vague: palat dyemi ani 'I might read (someday)'. The difference between this and the concessive tense is not clear; use of this form seems to convey greater determination to perform the action.
dyu
The interrogative particle. This particle is used to turn declarative sentences into questions of fact. It is the last word in the sentence: papul sensetl dyu 'Will the teacher come?'
hazu
Indicates that the speaker is performing contrary to expectation: ulat hazu ani 'I supposed to be reading (but I'm not)'.
kdasi
Asks for cooperation with the speaker. It is a polite intensifier of requests. The main verb is in the polite imperative. This particle usually stands at the end of the sentence, but not usually after the verb: dapul Du kdasi 'Please come'.
ker
Indicates desire. It immediately follows the verb. With the potentative mode, it means 'like to':umolat ker ani 'I like to read'. With the initiative, it means 'want to':uCalat ker ani = ukrelat ani 'I want to read'. This can also be expressed by the desiderative mode; the particle formation is more common in formal written contexts.
moce
This particle with any tense of the verb indicates consideration of an action: ulat moce ani 'I thinking about/considering/planning on reading'.
mZali
Expresses the speaker's regret about prohibiting an action. In this, it functions as a polite negative command. The action prohibited is used in the negative form of the indicative (unmarked) mode. This particle usually comes at the beginning of the sentence, but does not usually follow the verb: mZali upulak Du 'I'm sorry, but you cannot go.'
nocyo
Indicates that the speaker's action is not what it appears to be, or that the speaker is unsure about another's action: ulat nocyo ani 'I appear to be reading (but I'm not)'; ulat nocyo IMu 'It looks like he's reading (but I'm not sure)'.
Nyo
This particle indicates the imminent onset of an action. The initiative mode intensifies this sense: ulat Nyo ani 'I'm about to read'; uCalat Nyo ani 'I'm just about to read (any second now)'.
olZ
This particle always follows immediately after the verb. When used with a verb in the initiative mode, it indicates the compulsion to perform an action, or 'must': uCapul olZ ani 'I must go'. When used with the concessive tense, it indicates an obligation to perform an action, or 'should, ought to': dapul olZ ani 'I should go'. Since the concessive exists only in the present tense, a periphrastic form must be used for other tenses: da olZ, bUn Repul ani 'I should have gone.'
ya
This is the vocative particle. In normal speech, it is used to get someone's attention. It follows the name of the person being addressed (or the first term of the name, if multiple names or titles are used): noj ya 'Hey, Noj!'; danelwegi ya tereNo 'O terengo danelwegi!'; prabaset ya poSuSa 'O Emperor Prabaset!'. A noun in the vocative can take any postposition: udar ani canSaNa Di, poli ya aLaDap 'I praise You, O Good God!'. The vocative also allows one to move nouns out of their normal position; in this case, the regular postpositions are not required: noj ya, uvId ani Da 'I see you, Noj!' In theory, every time a person is addressed by name or title, the vocative particle should be used, but it is frequently omitted in informal speech.
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Locative Expressions

Postpositions

Locative expressions indicate where the action of the main verb takes place. Most Vogu locatives are built on locative postpositions. Some locative postpositions indicate location and direction, others indicate only location or direction (some also have non-locative meanings, which we do not consider in this section).

Multiple Noun Locatives

Some locative expressions specify a part of a larger location. In English, these are phrases of the type "on the top of the mountain", "to the bottom of the hill", etc., where the specific location (top, bottom) receives the locative preposition (on, to), and the more general location (mountain, hill) is related to the more specific by "of". In Vogu, however, both locations receive the same locative postposition and are paired together, with the more general location listed first: tranuQm patIseQm 'on the top of the mountain', DanuS topodiS 'to the bottom of the hill.'

Derived Adverbs

Most locative adverbs are formed by compounding a noun plus postposition. Some of these compounds are very old features of the language and so eroded that their components aren't always obvious. Although Vogu locative adverbs are more specific than their English counterparts (Vogu has, for example nasbri 'here', and nasbiS 'to here', where English has only "here"), the language can't accomodate ahead of time all the possible combinations of noun + postposition that might be required, so locative adverbs have simple noun counterparts, to which postpositions can be added. These are simple noun formations and do not display the eroding of their elements that the fixed compounds do:

Locative Particles

Locative particles are used to supply even greater specificity oflocation. They can be used with adverbs or postpositional noun phrases. They generally do not stand alone except in a few fixed phrases, such as ma ge ani 'Here I am!' and gu dyum 'Bottoms up!'. They follow the adverb or noun, and can be used to specify either location or motion. Sometimes they convey an intensifying effect, as in nasbri ma 'right here' (as opposed to simple nasbri 'here(abouts)'), other times they modify the meaning of the locative phrase: hwiSoQm mu 'in front of the house', tiwiQm ke 'next to the tree', nasbri ke u miba 'Mother is here alongside (presumably, me)'.

Locative particles are primarily a feature of colloquial speech and writing. Most particles have postpositional equivalents which are more commonly used in formal speech and writing: hwiSobla 'in front of the house'.

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Time Expressions

Relative Time

Vogu uses postpositions to express time relationships relative to some other time. These can be used with clock time or with more general time stamps, although many of the most common timestamps have fixed forms (usually highly eroded). The most common postpositions are

These are generally identical to the "conjunctive postpositions" noted in the section on subordinate phrases, but there are some differences.

Derived Adverbs

Many of the most common timestamp words in Vogu are formed from nouns plus postpositions, often highly eroded and sometimes with archaic usages of the elements. As with locatives, in order to accomodate any possible use of these timestamps, the time words exist in simple and compound noun forms, to which the temporal postpositions above can be added, to express any desired time relationship.

Note phrases such as jomLubkri lwokri 'last night' (lit. 'yesterday at night'). These parallel the locative formation for identifying a specific element of a whole. The more general time period is stated first, followed by the more specific part of it.

Temporal Particles

Temporal particles are adverbial particles used as time stamps. Unlike the locative particles, these are generally used by themselves, without the corresponding derived adverb:syeC upul avek = katbri upul avek 'a man is coming now'. Use of both seems foolish to the Kadanë, like a double negative in English (eg., "I'm not never going to"). Like the locatives, their use is restricted to colloquial speech and writing; for more formal applications, the derived adverbs are used.

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Verbs of Quality

Vogu often distinguishes between state or qualities that are temporary and those which are permanent. Some adjectives and nouns of state or quality have corresponding verbal forms (not predicate adjectives, but true verbs). In these cases, one generally uses the adjective, or noun in a possession idiom with -eta for the temporary state, and the true verb for a permanent one:

gonM 'be ill' (adj)
ugonM IMu 'He is feeling sick.'
yokonM 'sickness'
yokonM IMuta 'He is sick (now).'
fonM 'be ill' (v)
ufonM IMu 'He is (always) sick.'
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Numbers

Cardinal Numbers

The Kadanë numbering system is a base-5 system. In transcription, the numerals 0, 1, 2, 3, 4 are the only ones used. The following list gives the names of the numbers. At the end of the paper is a chart for converting base-10 to base-5 and vice-versa.

       Base-10       Base-5   Names            Collective Terms
         0              0     nok
         1              1     aQ
         2              2     naQ
         3              3     taQ
         4              4     goQ
         5             10     apoN             bupoN
         6             11     apoNIQ
         7             12     apoNaQ
         8             13     apoNtaQ
         9             14     apoNgoQ
         10            20     napoN            napobj
         11            21     napoNIQ
         12            22     napoNaQ
         15            30     tapoN
         20            40     gopoN            avek
         25           100     apoNpoN          popobj
         26           101     apoNpoNIQ
         27           102     apoNpoNaQ
         30           110     apoNpoN apoN
         31           111     apoNpoN apoNIQ
         35           120     apoNpoN napoN
         50           200     napoNpoN
         75           300     tapoNpoN
         100          400     gopoNpoN
         125         1000     tabjpoN          vovek
         250         2000     naQtabjoN
         375         3000     taQtabjpoN
         625        10000     gobjpoN
         3125      100000     apobjpoN
        15625     1000000     apoNIQpoN
        78125    10000000     apoNaQpoN
       390625   100000000     apoNtaQpoN
      1953125  1000000000     apoNgoQpoN
      9765625 10000000000     napobjpoN

The cardinal numbers are used for most requirements; the collective terms are used to render approximate amounts (bupoN 'around five').

The underlying principle of number formation is that powers of 5 are represented by base elements. Multiples of each power of 5 are shown by number fragments prefixed to the base element. Lower digits within a given power of 5 are shown by number elements following the basic element, either suffixed or standing alone.

  1. For the powers of 5:
  2. For lower digits:

Numbers are considered nouns in Vogu and can take postpositions. Compound numbers (i.e. numbers made up of separate words) are considered appositional phrases and as such only the first element in the number takes a postposition.

Numbers can also take adjectives. The noun complement of aQ is a-; that of the rest of the numbers is ka-. However, if the number is being used as a substitute for a common noun, the noun complement of the implied noun is used, instead. If a dependent adjective is used with a number, it is suffixed to the number, not to any following nouns; it can also be used independently immediately after the number).

Nouns following the numbers take the suffix -u, which predominates in vowel strength but does not attract the accent: apoNpoNIQotebav Dabmagu 'using these twenty-six books'. Note that nouns do not need the pluralizing suffix -INu when their number is explicitly stated.

Cardinal numbers can also be used independently to stand in for common nouns after their first reference. As noted, such substantive formations take the noun complement proper to the inferred noun. They can also take whatever postposition is appropriate to the noun.

            aQ Dabmagu              one book
            apoNtaQ poveku          eight men
            tabjpoNeta apoN miveku  with 130 women     
            naQ nakiznu naLaDap     two good knives
            taQoteb NuntaSu         these three pencils
            goQ miLaDapu            four good women
            Repul goQ               four (persons) went

Ordinal Numbers

Ordinal numbers are formed from the cardinal numbers by addition of the prefix ce-, eg. caQ 'first', cegobjpoN '625th'. They can be used as adjectives or adverbs. As adjectives, they function like other adjectives and follow the noun they modify with proper noun complement: mivek micapoN 'fifth woman'. There is an alternative to caQ, ceGitIs, which means both 'first in a sequence' and 'main'.

The ordinal numbers can be used without noun complement as adverbs indicating sequence of events: caQ palat ani, cenaQ papleSt 'First I will read, then I will eat'; ceGitIs vire ge Sara 'First/the main thing is, catch the ball!'

Another type of adjective can be formed from the cardinal numbers plus the word-forming prefix ge-. These adjectives indicate multiples. Many of them are used as substantives and have idiomatic meanings. When used adverbially, this adjective means 'in the manner of'; eg. genaQ 'by twos'.

        Cwan DagnaQ          double bed
        pogaQ                bachelor (lit. singleton)
        agnaQ                twins
        agtaQ                trinity, triumvirate
        kIpultyo INu gapoNIQ They left in groups of 6

A special form of this adjective, the future causative participle of the predicate used adverbially, means 'to divide into X parts': eg. from taQ 'three' -> getaQ 'triple' -> hisregtaQ 'into three parts': uraQu IMu kapleSta hisregapoNIQ 'He divided the food six ways.'

Collective Nouns

Collective numbers are nouns that imply quantities without actually specifying them. Some collectives are listed in the chart above; other common ones are

        vovek   'group'                 avek    'score (20)'
        yumoSt  'a lot'                 Costki  'remainder'
                        buli    'all'

These nouns may take postpositions and adjectives (noun complement ka-) like any other noun. Since they are considered a type of numeral in Vogu, any following noun must receive the number suffix -u like any other number: Costki Dabmagu 'the rest of the books'. Like other numerals, they also have ordinal forms in ce-:

        Costki Dabmagu     rest of the books
        Dabmag DacCostki   remaining books

Numbers in Word Formation

One often encounters numbers, especially number fragments, used in word formation: natmIQ 'union, unity'.

Expressions Using Numbers

To express selection out of a group, the postposition -Ikm is used. Compare: apoN povekIkm 'five of the men', apoN poveku 'five men'.

To express multiplicity of a quantity, use the postposition -av with the cardinal number: nagul apoNIQav 'six-fold increase'. To express multiplicity of events, use the postposition -etl with the cardinal number: Repyet IMu goQetl 'He sang four times.'

To express distribution of a quantity over a group, use the postposition -etl: dazbloS avek apoNetl Dabmaga 'Take five books per person (Lit. Each person take a book five times)'. To express distribution over time, use the postposition -eQm: dapleSt CoSa jojyomeQm 'Take one tablet per day;' dapleSt naQa CoSu jojyomeQm goQetl 'Take two tablets four times per day'

When counting out in Vogu, it is normal to replace 'one' with the word Dav 'a time': Dav, naQ, taQ, goQ, apoN 'one, two, three, four, five...'

Mathematics

The mathematical operations and the words used for them are listed below.

        Addition        -eta
        Subtraction     -ank
        Multiplication  -If
        Division        -av
        Equality        u
        Negativity      pItaS

        u taQ aQ e naQ      1 + 2 = 3
        u naQ taQ aQank     3 - 1 = 2
        u goQ naQ naQIf     2 * 2 = 4
        u taQ apoNIQ naQav  6 / 2 = 3 
        apoN kaptaS         -5

Remainder in division is indicated by the word hadupleStak 'uneaten': eg. u apoN napoNtaQ naQav e taQ kahadupleStak 'Thirteen divided by two is five with three left over.'

Fractions are expressed by their own words, formed from the cardinal numbers and the derivational suffix --zn. When used alone (e.g. '1/3rd'), these behave like numbers, and the following noun takes the suffix -u. When they are used as multiples of the fraction (eg. '2/3rds'), the multiple is given as a preceding number, the fraction behaves like a noun and takes suffix -u, and any following noun takes the distributive postposition -Ikm. In any phrase involving a numerator of 1 (1/2, 1/3, etc.), aQ is understood and is included only in formal or technical writing. If whole numbers are used with fractions, the fraction takes the postposition -eta.

        nazn       1/2    tazn              1/3
        gozn       1/4    apozn             1/5
        apoNIzn    1/6    apoNazn           1/7
        aQ nazneta 1 1/2  naQ goQeta apoznu 2 4/5
        
            nazn rablowu   'half an apple'
            naQ taznu rablowakm '2/3rds of an apple'

Decimals are expressed as fractions of powers of 5. Recall that the number to the right of the decimal place is in base 5: the first place represents 5-1, the second 5-2, etc. In English, these numerals must be expressed as fractions of 5, eg.: 10.25 apoN naQeta apoznu '5 and 2 fifths'; 10.025 apoN naQeta apoNpoznu '5 and 2 twenty-fifths.'

The Vogu equivalent of the English term 'per cent' is the word tabjItapo. Of course, since Vogu uses base 5, this word does not mean 'one-hundreth part' but 'one-hundred twenty fifth part'. tabjItapo is considered a noun and takes the numerative suffix -u: apoNpoN tabjItapu '25 tabjihtapo = 20 per cent.'

To express powers of a number, use the word tabj 'count' for the exponent and the postposition -If for the quotient: 325 naQ tabju taQIf 'three squared', 1010005 tabjpoN tabju apoNIf 'five to the one-hundred-twenty-fifth (5125).'

Base Conversion Chart

While we will not go deeply into the theory of bases here, and an understanding of bases isn't necessary to be able to count in Vogu, a brief overview of base theory may be in order.

The concept of numerical base and place notation are closely linked. In any numbering system which uses place notation (unlike, say, ancient Greek, which had different symbols for 10, 100, 1000, etc.), the value of a number is determined by multiplying each digit of the number by the power of the base represented by each column of the number. You may recall your grade-school math teacher breaking down a number like 234 by describing it as '2 in the hundreds column, 3 in the tens column, 4 in the ones column.' To put it more formally, (2 * 102) + (3 * 101) + (4 * 100) (X0 = 1).

Arabic numerals (our own numbering system) use base 10: beginning at the right, each subsequent column to the left in the number represents one more power of 10; each power of 10 is multiplied by the digit found in that column. Vogu uses base 5. The concept of place notation and multiplying by the digit remain the same, but each column of the number represents another power of 5. The number 234 from above could be a valid Vogu number, but its value in base 5 is 2345 = (2 * 52) + (3 * 51) + (4 * 50) = 6910.

A numbering system always uses the same number of digits as its power: the base 10 Arabic system uses digits 0 - 9, while the base 5 Vogu system uses 0 - 4. (In a similar fashion, the base 2 binary system uses only 0 - 1 and the base 16 hexadecimal system uses 0 - F.)

The student is advised to forget most of this theory and simply memorize the Vogu numbers by counting, visualizing if possible both the Vogu and Arabic numerals corresponding to the spoken number. This will generally be sufficient for most every-day counting purposes. The table below can be used as a relatively quick way to convert larger numbers between the two bases.

Col 11 10 9 8 7 6 5 4 3 2 1
Power 510 59 58 57 56 55 54 53 52 51 50
15 9,765,625 1,953,125 390,625 78,125 15,625 3,125 625 125 25 5 1
25 19,531,250 3,906,250 781,250 156,250 31,250 6,250 1250 250 50 10 2
35 29,296,875 5,859,375 1,171,875 234,375 46,875 9,375 1,875 375 75 15 3
45 39,062,500 7,812,500 1,562,500 312,500 62,500 12,500 2,500 500 100 20 4

Base 5 to Base 10
For each digit of the Vogu number (beginning on the right), locate the decimal value at the intersection of the row corresponding to the digit and the column corresponding to the place on the Vogu number. Skip columns containing a 0. Add together the decimal values of all columns to determine the decimal equivalent.

3025:
For the first place of the number, find the value '2' corresponding to the decimal value in the table at the intersection of column 1, row 2.
Skip the second place, since it is 0
For the third place of the number, find the value '75' in the table at the intersection of column 3 and row 3.
Add the decimal values together to get 3025 = 7710.
Base 10 to Base 5
Find the closest approximation to the decimal number in the table. Record the digit from this row in the Vogu number place corresponding to the column in which the number was found. Subtract this number from the original number. Find the closest approximation to the remaining decimal number and record its digit in the appropriate place in the Vogu number. Enter a 0 in any place that you skip a column (i.e. power of 5). Subtract the second number from the remainder. Continue this process until you have a remainder less than 5. Place this remainder in the right-most (ones) place of the Vogu number.

7710
Find the closest approximation to 77, which is 75. Place the digit '3' (corresponding to the row) in place 3 (corresponding to the column) of the Vogu number. Subtract 77 - 75 = 2: '3xx'.
Since there is no approximation in column 2 of the table, place a '0' in place 2 of the Vogu number: '30x'.
Since we are left with a remainder less than 5, place the digit '2' in the right-most (ones) place of the Vogu number: '302'.
Decimals
Decimals (pentimals, in Vogu) can be converted in the same way by counting the columns of the number after the decimal point in reverse; keep in mind that the first column after the pentimal point is 5-1: .025 = ((0 * 5-1) + (2 * 5-2)) = 2/2510.

© 1998, Terrence Donnelly

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