Title: Nomenclature
Description: How to say numbers non-decimally
uaxuctum - April 21, 2007 06:23 AM (GMT)
In my opinion, the issue of dozenal nomenclature is not just something accesory that one might leave aside unresolved until the use of the dozenal base catches on, but a crucial issue if dozenal is ever to take off, since one of the first and most off-putting hurdles the average person finds when trying to use a different number base is precisely the fact of being unable to
read the numbers. Decimal seems so "natural" not least because it reflects how (most of) our languages name numbers. Writing decimal "123" is analogous to saying "one hundred and twenty-three" in English, so decimal numbering seems immediately "intuitive" to English speakers, because that's the very way their own language names and organizes numbers. The very fact of English possessing a decimal nomenclature makes it easy for its speakers to
conceptualize and talk about numbers decimally. Similarly, the lack of proper nomenclature for the hexadecimal base means that computer science students confronted with a number like "F3C" do not even know how to
say it, so they will usually spell it out ("eff-three-cee") as if it were some kind of arcane code, rather than read it and perceive it as an actual number, as an actual
quantity. Or worse, if they try to read hex "32" like a number, they will resort to decimal nomenclature saying "thirty-two" and thus inevitably misconceptualizing it. So, for people who use hex to be able to actually start to
think in hex, rather than just write digits without actually conceptualizing its numerical meaning, the first thing they need is precisely to be able to
talk in hex, to be able to codify hex numbers linguistically. They are in need of hex number
words, which surprisingly it seems no one has yet come up with; a clear symptom that, even though hex numbers are common in the computer world, actual "thinking in hexadecimal" by its users is extremely rare. They just use hex numbers as mere strings of symbols without actually
understanding what quantities those digit strings actually refer to; sometimes even using them as mere code-words, as in the case of "DEADBEEF" (this is known as
hexspeak). A similar situation we encounter for dozenal, although at least in this case English has already developed a partial (far from complete or satisfactory) nomenclature system.
It is not hard to find proposals for English dozenal nomenclature in dozenalist websites (including this forum), but if dozenal is meant to ever become widely used internationally there should also exist proposals for dozenal nomenclature in other languages, at least for widely-used ones such as Spanish, French, German, Russian, Hindi, Arabic, Chinese or Japanese. I think once I found somewhere something regarding French and German dozenal number proposals, but I can't recall where. I myself have devised dozenal and hexadecimal (and even an attempt at binary) number names for my own native language (Spanish), a proposal which I will explain in my next post. One thing I take issue with many nomenclature proposals I've seen so far is that they rarely attempt to be anything more than a collection of fancy names made up by its inventor without trying to support them on something more objective than their subjective taste. My proposal addresses this objection by coming up with the missing nomenclature through a process of linguistic "reconstruction".
Shaun - April 21, 2007 08:13 AM (GMT)
The best French suggestion came from Jean Essig in his "Douze, Notre Dix Futur".
I'll post the details when I find my copy of his book.
One German suggestion included "jar" (from Jahr = year) for twelve, so *11 is jar-eins for example.
uaxuctum - April 21, 2007 07:54 PM (GMT)
Before describing my proposal, I will first offer an overview of the way Spanish names (decimal) numbers, for the benefit of those who are not familiar with this language. We have independent roots for quantities up to ten and for powers of ten: 0 cero, 1 uno, 2 dos, 3 tres, 4 cuatro, 5 cinco, 6 seis, 7 siete, 8 ocho, 9 nueve, 10 diez, 100 cien[to], 1000 mil, [10.000 miríada], 1.000.000 millón, [1.000.000.000 millardo], 1.000.000.000.000 billón, 1.000.000.000.000.000.000 trillón, etc. (note I've used a point as the thousands-separator because this is the usual convention in Spanish, except in U.S.-influenced Mexico; same for the long-count interpretation of the -illion terms). It is already known that cien is etymologically a derived word from the ancestor form of diez, but this is totally obscure in the modern language (same in English for "hundred"). Some have proposed the words nueve "nine" and nuevo "new" (both the Spanish and English ones) go back to Proto-Indoeuropean derivatives from the same root *new- ("now"), which would suggest a very early non-decimal, octal counting.
Then, we use recognizably derived but nonetheless unique names for eleven to fifteen: 11 once, 12 doce, 13 trece, 14 catorce, 15 quince; and for the tens: 20 veinte, 30 treinta, 40 cuarenta, 50 cincuenta, 60 sesenta, 70 setenta, 80 ochenta, 90 noventa. In these, the deriving suffix (+10 -ce, ×10 -inte/-inta/-enta) is currently obscure; in the case of veinte, the root is also obscure, while it is partially obscured in once, catorce and quince (although for these it's not difficult to establish the connection with 1 uno, 4 cuatro and 5º quinto). The names of other numbers are transparent compounds, with the only exception of 500 quinientos (as with 15 quince, this one shares its root with the ordinal number 5º quinto; which is etymologically the same root as that of 5 cinco, although to modern speakers the roots cinc- and quin- merely appear similar rather than regularly related). The compounds for the other teens and for the twenties suffix the relevant digit, using -i- (from the conjunction y meaning "and") as the connecting vowel: 16 dieciséis, 17 diecisiete, 18 dieciocho, 19 diecinueve, 21 veintiuno, 22 veintidós, 23 veintitrés, 24 veinticuatro, 25 veinticinco, 26 veintiséis, 27 veintisiete, 28 veintiocho, 29 veintinueve). The compounds for other tens work the same, but the elements are treated as separate words: 31 treinta y uno, 32 treinta y dos, 43 cuarenta y tres, etc. The two last digits in higher numbers simply follow the rest of the number: 108 ciento ocho, 120 ciento veinte, 144 ciento cuarenta y cuatro, 432 cuatrocientos treinta y dos, 864 ochocientos sesenta y cuatro, etc. The hundreds prefix the relevant digit, with monophthongized root vowel in the case of 7 and 9 (vocalic alternations between the stressed diphthongs ie or ue, and the unstressed monophthongs e/i or o/u, are common in the language and are the reflex of Vulgar Latin mid-open vowels): 200 doscientos, 300 trescientos, 400 cuatrocientos, 600 seiscientos, 700 setecientos, 800 ochocientos, 900 novecientos. For the thousands, just precede the relevant number as a separate word: 2.000 dos mil, 3.000 tres mil, 15.000 quince mil, 20.000 veinte mil, 35.000 treinta y cinco mil, 123.000 ciento veintitrés mil, etc.
Things start to get a little tricky with ordinal numbers. Like in English, 1º primero and 2º segundo have unique names (I'm citing only the masculine forms, but in all cases there are corresponding feminine forms ending in -a: 1ª primera, etc., as well as plural forms). Of these, segundo is clearly related to the verb seguir "to follow", while primero belongs to a family of words that includes primicia, primordial, primitivo, primigenio, etc. (both roots can be found in related English words of Latinate origin). Other ordinals are derived from the corresponding numbers by means of a suffix, which can be -ero (1º primero, 3º tercero), -io (3º tercio, this form is rare as an ordinal), -to (4º cuarto, 5º quinto, 6º sexto), -avo (8º octavo), -eno (9º noveno), -imo (7º séptimo, 10º décimo) or most commonly -ésimo (20º vigésimo, 30º trigésimo, 40º cuadragésimo, 50º quincuagésimo, 60º sexagésimo, 70º septuagésimo, 80º octogésimo, 90º nonagésimo, 100º centésimo, 200º ducentésimo, 300º tricentésimo, 400º cuadringentésimo, 500º quingentésimo, 600º sexcentésimo, 700º septingentésimo, 800º octingentésimo, 900º noningentésimo, 1.000º milésimo, 10.000º diezmilésimo, 100.000º cienmilésimo, 1.000.000º millonésimo, etc.). For the teens, in some cases there are alternative forms with a different suffix or even with a different order of the elements: 11º undécimo/onceno, 12º duodécimo/doceno, 13º decimotercero/decimotercio/tridécimo/treceno, 14º decimocuarto/catorceno, 15º decimoquinto/quinceno, 16º decimosexto, 17º decimoséptimo, 18º decimoctavo, 19º decimonoveno. In the case of compounds, all elements appear in ordinal form (unlike in English where only the last element is suffixed): 25º vigésimo quinto, 72º septuagésimo segundo, 101º centésimo primero, etc. The tricky part is in the capricious unpredictability of the suffix and in the irregular changes undergone by the root, which often appears under an archaic Latin-looking form. Some of these root changes, particularly those for the higher tens and for the hundreds, can be so arcane that many speakers cannot remember them, or confuse them, or have never even heard them; e.g., 3.456º is properly tresmilésimo cuadringentésimo quincuagésimo sexto, but most, even those who actually know the ordinal form, will avoid it and substitute the less arcane cardinal form, thus saying el tres mil cuatrocientos cincuenta y seis instead, meaning "the 3,456 one".
In the case of fractions, 1/2 has its own names (la mitad, un medio), while for others the denominator is expressed through a derivation, which in some cases coincides with the ordinal (1/4 un cuarto, 1/5 un quinto, 1/6 un sexto), while in others it uses the suffix -avo (e.g., 1/12 un doceavo, 1/16 un dieciseisavo, 1/20 un veinteavo); but again there are irregularities (1/3 is always un tercio and never *un tercero) and alternative forms (e.g., 1/100 can be read un centavo, un céntimo, but most commonly una centésima parte). The usual convention in Spanish is the decimal comma, so for 3/4 we write 0.75 and read cero coma setenta y cinco [centavos/céntimos/centésimas] (usually centavos in the Americas and céntimos in Spain are reserved for "cents"). Per cent and percentage are por cien[to] and porcentaje, so 50% is read cincuenta por ciento or cincuenta por cien (100% is almost always read cien por cien).
Then, there's the collectives, some with unique derivations such as dúo and trío/terna, but typically formed with the suffixes -eto (as in dueto, terceto, cuarteto, quinteto, sexteto) or -ena (as in decena, docena, quincena, centena). Note English "dozen" is related to docena (although it entered English through its French cognate). And then, there are derivatives such as ternario from terna, decimal from décimo, nonagenario from *nonageno (for nonagésimo), etc., whose meaning should be obvious to English speakers. The Spanish equivalent of the English neologism "dozenal" is obviously docenal.
uaxuctum - April 21, 2007 07:56 PM (GMT)
| QUOTE (Shaun @ Apr 21 2007, 08:13 AM) |
| One German suggestion included "jar" (from Jahr = year) for twelve, so *11 is jar-eins for example. |
I don't think people immediately associate "year" with 12, at least not anymore than they would associate it with 52 or 365. To me, "year" first evokes a large number like 365, rather than a relatively small one like 12. OTOH, it wouldn't hurt to have a unique name for the versatile number 360, which is very near the number of days in a year, so the proposed jar ("yar" in English) might fit for this quantity, better than for twelve. So we could now say there are "one yar degrees to the circle". ;)
For twelve, I'd much rather go for something like dutz from Dutzend. But really, German is not in need of another unique name for twelve, because it already has one: zwölf, or two if we count the collective noun Dutzend. So why not just *11 einßwölf, *12 zweizwölf, *13 dreizwölf, *14 vierzwölf, etc., analogously to 13 dreizehn, 14 vierzehn, etc.? Although the suffix -dutz could be used as the dozenal equivalent of -zig: *20 zwandutz, *30 dreidutz, *40 vierdutz, etc.
Ebbe - April 23, 2007 09:03 AM (GMT)
| QUOTE (uaxuctum @ Apr 21 2007, 08:56 PM) |
| For twelve, I'd much rather go for something like dutz from Dutzend. But really, German is not in need of another unique name for twelve, because it already has one: zwölf, or two if we count the collective noun Dutzend. |
Well. I would always prefer the Dutzend. Perhaps zwölf could be used, but there are combinations which are a bit hard to pronounce, and not well-sounding either: einszwölf (*11) and sechszwölf (*16).
Probably Dutzend would eventually be spoken just as Dutz, just as you propose.
| QUOTE |
| So why not just *11 einßwölf, *12 zweizwölf, *13 dreizwölf, *14 vierzwölf, etc., analogously to 13 dreizehn, 14 vierzehn, etc.? Although the suffix -dutz could be used as the dozenal equivalent of -zig: *20 zwandutz, *30 dreidutz, *40 vierdutz, etc. |
Well, that indicates you would like to keep our curious way of speaking the ones before the tens. I disagree. Introducing dozenal would be a great opportunity to do away with it. There is, in fact, a club "Verein Zwanzigeins" in Germany which promotes just that (www.verein-zwanzigeins.de - only in German).
So *11 would be Dutzend-eins, *12 Dutzend-zwei and so on, *20 zwei Dutzend etc. For *100 we already have the Gros. For *1000, German wikipedia gives Maß, but I never heard of that. I would prefer Dozen gross. For *10000 we could adopt your zyriad for Zyriade, *100000 Dutzend Zyriaden, *1000000 Zillion and so on.
In Czech there is a word tucet for dozen, and veletucet (from velký tucet - great dozen) for gross. A problem is that they don't have a special name for eleven. It's just jedenáct "oneteen".
Apart from that, everything would be the easy: (Edit: This forum doesn't seem to display all the characters correctly, so i use them without diacritics)
1 jeden 2 dva 3 tri 4 ctyri 5 pet 6 sest 7 sedm 8 osm 9 devet *T deset *E ? *10 tucet *11 tucet jeden *12 tucet dva ... *20 dva tucty *30 tri tucty *40 ctyri tucty *50 pet tuctu *60 sest tuctu ... *100 veletucet.
Notice the change after *40: The Czech language use the nominative singular after 1, the nominative plural after 2-4, and the genitive plural after 5: pet tuctu "five of dozens" (Russian is similar, instead they use genitive singular after 2-4, which is in fact an old dual form).
Well, I'm still struggling to learn that language, so much of this is perhaps only nonsense.
icarus - April 23, 2007 02:04 PM (GMT)
Nomenclature is important because if we are to fully use dozenal, we need to communicate it, and much of the communication would be spoken. The Dozenal Society of America examined two contrasting philosophies regarding nomenclature in the mid forties. The actual usage of these philosophies appear to have been in play for sevral years before the time this article was written
The following is an excerpt from an article in the Duodecimal Bulletin, whole number 3, pages *b through *11, published in 1945 by the Duodecimal Society of America, now the Dozenal Society of America. This article is posted here with permission of the Society.
"Members of the Duodecimal Society are somewhat accustomed to the mention of the Principle of Least Change, and the Principle of Separate Identity. But comment from the members seems to show that a clearer exposition of these principles would be appreciated.
"Since it is important that these principles, and the divergence which they represent, be thoroughly understood so that they may be advantageously applied, an attempt will be made to bring these principles into better definition.
"Duodecimal proposals divide themselves, readily, into two groups. These groups are named for the principle which typifies each.
"Classification under the Principle of Least Change
"Most duodecimal proposals are conceived with the fundamental purpose of making that specific proposal most acceptable to the mind of the general public. They are quite easily characterized as embodying the Principle of Least Change.
"They usually contemplate no change in the names and the symbols for the first nine numbers, and sometimes propose to retain the customary names for ten and eleven when used duodecimally.
"They exhibit a similar approach to the duodecimal weights and measures. The sizes and names of the accepted Anglo-American standards are retained as faithfully as possible, and these are adjusted by minor changes into a duodecimally unified metric system.
"Classification under the Principle of Separate Identity
"The outstanding characteristic of duodecimal proposals that fall within this group, is that they are designed to prevent any possible confusion with decimal quantities or measures. They generally propose entirely new symbols for all numbers and new names for these numbers.
"Since they already embrace the necessity for complete change, they afford the opportunity for the suggestion of every novel practice and method that may seem to improve our current procedures. New practices in grouping, denominating, and punctuating numbers are typical.
(Note: Page 10;)
"There is a corresponding revisionary attitude as to the weights and measures. These are generally to be based upon some specific method of determining a new unit of length, and around this unit is erected a conformal duodecimal metric system.
"Traits typical of this group, then, are the general disregard of customary methods and practices, and the proposal of radical and novel procedures in numeration, notation, nomenclature and metrology.
"Rationale
"These classifications seem simple and clear. But confusion will continue unless it is comprehended that this separation means more than it first appears. There is a fundamental difference in ideologies involved.
"As one becomes more familiar with duodecimals, and duodecimal proposals, one begins to perceive that there are supporting factors for both groups. One begins to see that in some applications there would be greater advantage in the one type of system than in the other. And that under other conditions, the reverse would be true, and that what had been considered essential had become secondary.
"As an analogy, the general public makes little use of the Kelvin Temperature Scale which is based on Absolute Zero, but prefers a scale emphasizing the freezing and boiling points of water. For some scientists, however, there are advantages in the use of the Kelvin Scale which make in indispensable.
"It must be realized that it is from the proposals under the Principle of Separate Identity that the innovations and inventions are developed which constitute progress. And these new ideas are valuable. But to the general public, the idea of changing all the names and symbols for numbers would be simply repulsive, and entirely unthinkable, and proposals involving as little change as possible are required.
"So both systems are necessary. It should be the responsibility of the Society to develop both. And when a practical degree of unanimity is expressed in a proposal under either of the two principles, that proposal should be endorsed by the Society. It must be clear that such endorsement does not mean acceptance of the one principle and the suppression of the other. Nor does it imply the necessity of blending both principles into a single solution. Both are necessary. Both are important. But they are opposed, and relatively unblendable.
"Different necessities, different viewpoints, different logics, are inherent in each. We will only create confusion and useless dissension if we apply to some proposal under the Principle of Least Change the arguments and critiques that are
(Note: Page *11;)
entirely proper to the Principle of Separate Identity. And the reverse. This just won’t work. Since opposed lines of thought are involved, there must be a corresponding change of attitude as we consider the one or the other.
"Since each of these groups has its own definite factors of preference, it would be well to avail ourselves of these advantages intelligently, - to analyze each new proposal from the viewpoint specifically proper to it, - and to aid in the development of a consensus as to each, by making our judgments known.
"Recently there has been a considerable amount of discussion of the duodecimal terms and symbols used by the Society. Perhaps it would be well to set forward the Society’s attitude in the matter.
"When formal organization of the Society was undertaken, it was decided that we would continue to use the Dek, El and Do, which, over a period of some eight or nine years, had become accepted as the usage of the informal society.
"All of the Society’s duodecimal material, currently in the hands of the public, employs this usage. Moreover, there is a solid basis for its preference. The symbol “X” for ten, was used exclusively throughout western civilization from early Roman days until the last years of the 13th Century. And all the European names for ten are derived from the Latin “decem,” pronounced “dekem.”
"When the weight of preference shifts to some other usage, and we can be confident of unanimity and finality in that choice, then the change should be made through official action of this Society. This possibility is not to be neglected. For this reason, there will be unbiased presentation of all such proposals, and the adoption of an accepted usage by the Society does not in the least preclude consideration of any and every proposal under the Principle of Least Change.
"For our personal use, of course, we shall employ those terms and symbols preferable to each of us. When any of our papers are selected for publication, it will be easy to substitute the accepted usage.
uaxuctum - April 24, 2007 05:22 AM (GMT)
Here's my proposal for Spanish dozenal nomenclature:
Currently Spanish has the terms docena, gruesa and gran gruesa corresponding to "dozen", "gross" and "great gross", but there are two problems with them: they are collective nouns rather than numerals (i.e., they belong to a different grammatical category, their decimal equivalents being decena, centena and millar, instead of diez, cien and mil), and just like in English they are hardly satisfactory as the basis for a fully functional nomenclature, because reading "123456" as una gruesa dos docenas y tres grandes gruesas, cuatro gruesas cinco docenas y seis, sounds even more convoluted and verbose than English "one gross two dozen three great-gross, four gross five dozen and six".
Now, rather than merely coming up with some arbitrary neologisms, my idea is to "reconstruct" the "what-if" scenario of Proto-Indoeuropean (PIE) speakers having hypothetically switched to dozenal counting, and then "evolve" the words that would have resulted in Latin and hence in Spanish.
First, let's have a look at the evolution of some Spanish numbers from Proto-Indoeuropean through Latin:
(I'll use capital letters for PIE syllabic sonorants and a colon for vowel length, so as to avoid diacritics.)
PIE *dekM > *dekem > Lat. DECEM > *deçe > Spa. diez (dec 10)
PIE *wi-dkM-ti: > *wi:kimti: > Lat. VI:GINTI: > *viinti > Spa. veinte (dec 20)
PIE *trY-dkM-ta: > *trikimta: > Lat. TRIGINTA: > *triinta > Spa. treinta (dec 30)
PIE *kwetwer-dkM-ta: > *kwetre:kimta: > Lat. QVADRA:GINTA: > *quadrainta > Spa. cuarenta (dec 40)
PIE *penkwe-dkM-ta: > *kwenkwe:kimta: > Lat. QVINQVA:GINTA: > *quinquainta > Spa. cincuenta (dec 50)
PIE *dkM-tom > *kemtom > Lat. CENTVM > *çentu > Spa. cien[to] (dec 100)
Now, let's see what could have happened if the Proto-Indoeuropeans had switched to dozenal. The most straightforward method for the switch would have been simply to substitute *d(u)wo-d(e)kM (twelve) for *d(e)kM (ten):
PIE *duwo-dekM > *du:odekem > Lat. DVODECIM > *dodeci > *doçi > Spa. doce (dec 12 / doz 10)
PIE *wi-dwo-dkM-ti: > *widwo:kimti: > Lat. *VIDO:GINTI: > *viointi > *veonte > Spa. *veunte (doz 20)
PIE *trY-dwo-dkM-ta: > *tridwo:kimta: > Lat. *TRIDO:GINTA: > *triointa > *treonta > Spa. *treunta (doz 30)
PIE *kwetwer-dwo-dkM-ta: > *kwetredwo:kimta: > Lat. *QVADRADO:GINTA: > *quadraointa > *cuarointa > Spa. *cuaronta (doz 40)
PIE *penkwe-dwo-dkM-ta: > *kwenkwedwo:kimta: > Lat. *QVINQVADO:GINTA: > *quinquaointa > *cincuointa > Spa. *cincuonta (doz 50)
PIE *dwo-dkM-tom > *dwo:kemtom > Lat. *DO:GENTVM > *doentu > Spa. *duen[to] (doz 100)
So we have just "reconstructed" some key terms from the hypothetical dozenal nomenclature that Spanish would have inherited had our remote ancestors switched to dozenal. If we compare the reconstructed dozenal terms with their decimal analogues (veinte vs. *veunte, cuarenta vs. *cuaronta, ciento vs. *duento), we find that basically they differ in their vocalism; where decimal has e/ie/ei (front unrounded vowels), dozenal has o/ue/eu (their corresponding back rounded vowels). With these reconstructed terms, and using analogy with the decimal system, we have enough already to reconstruct the whole series up to dozenal BBB:
| CODE |
Decimal
0 cero 10 diez 20 veinte 30 treinta 100 cien 1 uno 11 *dieciuno 21 veintiuno 31 treinta y uno 101 ciento uno 2 dos 12 *diecidós 22 veintidós 32 treinta y dos 200 doscientos 3 tres 13 *diecitrés 23 veintitrés 40 cuarenta 300 trescientos 4 cuatro 14 *diecicuatro 24 veinticuatro 41 cuarenta y uno 400 cuatrocientos 5 cinco 15 diecicinco 25 veinticinco 50 cincuenta 500 quinientos 6 seis 16 dieciséis 26 veintiseis 60 sesenta 600 seiscientos 7 siete 17 diecisiete 27 veintisiete 70 setenta 700 setecientos 8 ocho 18 dieciocho 28 veintiocho 80 ochenta 800 ochocientos 9 nueve 19 diecinueve 29 veintinueve 90 noventa 900 novecientos
|
| CODE |
Docenal
0 cero 10 doce 20 *veunte 30 *treunta 100 *duen 1 uno 11 *dociuno 21 *veuntiuno 31 *treunta y uno 101 *duento uno 2 dos 12 *docidós 22 *veuntidós 32 *treunta y dos 200 *dosduentos 3 tres 13 *docitrés 23 *veuntitrés 40 *cuaronta 300 *tresduentos 4 cuatro 14 *docicuatro 24 *veunticuatro 41 *cuaronta y uno 400 *cuatroduentos 5 cinco 15 *docicinco 25 *veunticinco 50 *cincuonta 500 *quinuentos 6 seis 16 *dociséis 26 *veuntiseis 60 *sesonta 600 *seisduentos 7 siete 17 *docisiete 27 *veuntisiete 70 *setonta 700 *seteduentos 8 ocho 18 *dociocho 28 *veuntiocho 80 *ochonta 800 *ochoduentos 9 nueve 19 *docinueve 29 *veuntinueve 90 *novonta 900 *noveduentos A diez 1A *docidiez 2A *veuntidiez A0 *dezonta A00 *deceduentos B once 1B *docionce 2B *veuntionce B0 *onzonta B00 *onceduentos
|
Since this dozenal nomenclature works analogously to the existing decimal one, thus respecting the idiomatic ways of naming numbers Spanish speakers are used to, and since the new terms look credibly like "genuine" Spanish words and are similar enough to the existing numerals so that they can be readily associated with their meaning, this proposal can be easily learned and accepted by native speakers.
For the thousands, I still haven't settled on a definitive proposal because the etymology of Latin mille is not clear (unlike for English thousand, which we know derives from a Germanic compound *thu:s-hundi meaning "swollen hundred"). Some have proposed mille derives from PIE *sm-i-ghslo-i, from *sem (meaning "one") and *gheslo (meaning "thousand", this is the ancestor root of "kilo"); but even if we accept this hypothesis we quickly find ourselves running down a dead-end alley, because we don't know how to analyze the root *gheslo and it doesn't appear to be in any way related to the root *dekM ("ten"). One solution to overcome this could be simply to apply the above mentioned "vowel-change rule" to the decimal term mil, but in my opinion the resulting dozenal term mul sounds ugly and doesn't have the "ring" of a Spanish numeral word. Another solution could be to backform zil from zillón, by analogy with mil > millón. The rationale for these dozenal "zillion" terms I have already explained in detail in another thread, so I won't repeat myself here. In Spanish, they would be: ziríada (10.000 / 1.0000), zillón (1.000.000 / 100.0000), zirión (100.000.000 / 1.0000.0000), zillardo (1.000.000.000 / 10.0000.0000), and dúgol (1.000.000.000.000 / 1.0000.0000.0000); remember I'm using a dot instead of a comma as the "thousands"-separator here, as this is the general convention in Spanish.
Going with the zil solution, which seems to me the much better of the above two, we could now read the dozenal number 123456789AB in Spanish as:
docidós zil tresduentos cuaronta y cinco zillones seisduentos setonta y ocho zil noveduentos dezonta y once
if we follow the "grouping-in-threes" or "Western" style (12.345.678.9AB), or alternatively as:
duento veuntitrés ziriones cuatrozil quinuentos sesonta y siete ziríadas ochozil noveduentos dezonta y once
if we follow the "grouping-in-fours" or "Eastern" style (123.4567.89AB). Both ways it sounds very recognizably like a number in Spanish; just compare with the decimal way to read 12.345.678.978:
doce mil trescientos cuarenta y cinco millones seiscientos setenta y ocho mil novecientos setenta y ocho
That is, this proposal would blend into the language almost effortlessly and painlessly, looking "natural" enough to native speakers and requiring only a few regular phonetic changes (cie- > due-; -ei- > -eu-; -e- > -o-; mi- > zi-), which in my opinion is a critical factor for its eventual acceptance. This is even more important when dealing with Spanish, because unlike English our language is not prone to readily accept neologisms unless they come from a traditional source like Greco-Latin roots. So the more unfamiliar or "un-Spanish" a new term or nomenclature system appears to native speakers, the less likely it is to be accepted into the language without resistance; and definitely the last thing we need if we want the dozenal idea to spread is to give people yet another reason to reject it. So the fewer changes we require them to get used to for the switch to dozenal, the better.
icarus - April 24, 2007 11:06 PM (GMT)
Very nice proposal Uaxactum, if it were a building, it would be a neotraditionalist masterpiece (like Leon Krier). Someone did some thorough research and creatively devised an educated system for Spanish based on what we know of history.
All I’ve done for English is add names for two digits and simply use the existing rank system. I use “dess” instead of “dek” (There aren’t too many English words with “ek” in it unless it is instead “deck”) and have adopted “ell” since 2003 by influence of y’all. Perhaps “dess” is a sawed-off “decimal” and “ell” the same for “eleven”. So desenty, ellenty, dess hundred, ell hundred, etc. You may know that the English “hundred” is not as strictly decimal as “kmtom” is, so its application to dozenal perhaps isn’t as illegitimate. (Hundred seemed to be stretched to fit *84, so I suppose one can stretch it to fit 144.) This usage of existing ranks vastly simplifies the nomenclature question. Many other languages have simply adapted the existing system of rank to new circumstances during base conversion. I think using "gross, great gross" is out of the question because it is clumsy, but manufacturing new ranks isn't as useful as coopting the present scheme. If we are confused, just say “dozenal” after your number. Until we have a brilliant neotraditional linguistic treatment for English á la Uaxactum, it’s six hundred ellenty four for a grand for me.
Maybe I’m making up reasons but the English-language neotraditional dozenal proposal would have to take into account that English has traveled away from its roots in a unique way, so that words taken from the Germanic roots seem musty and alien in the current context. One would have to play the Norman Conquest and Shakespeare on their neotraditional proposal. (i.e. Would the Anglosaxons have put "gh" and "th" and other utterances in the dozenal words...when the French invaded, how would they have modified the dozenal English words. Maybe the dozenal words wouldn't have been canned with thou and thy.) In the light of this fact I believe “dess” and “ell” are rather plausible (mainly because they are short and simple). I guess there aint no difference between dek and dess. Maybe I am wrong...
Either way nomenclature has to work in the current world, and the question of nomenclature should not interfere with application of dozenal when dozenal is practical.