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Counting and Measuring in Beoǧǧen
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A look at Beoǧǧen's duodecimal system and standard measures.
This public article was written by [Deactivated User], and last updated on 31 Aug 2016, 01:01.

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[edit] [top]Counting

Beoǧǧen is unlike any known natural language in that it counts in a pure duodecimal system. This means that instead of units, tens, hundreds, thousands (etc etc) columns, Beoǧǧen has units, twelves, one-hundred and forty fours, one-thousand seven-hundred and twenty eights and so on and so on - all multiples of twelve.



Therefore, if one were to write in duodecimal with arabic numerals, 10 would not represent ten, but twelve. Similarly, 24 would represent twenty-eight (i.e. two twelves and four) not twenty-four. For the purposes of discussing Beoǧǧen numbers with arabic numerals, we will use the TE convention - that is to say ten will be represented by T and eleven by E. Thus, 1T is twenty-two and 1E is twenty-three. We will also use the abbreviation DD for duodecimal to indicate the immediately succeeding number is written in duodecimal.
The base-12 counting system is a feature shared by all Gulfic languages, and so it is not possible to trace it’s origins. One can assume the Proto-Anan people developed this way of counting. As well as a common numeral system, Gulfic languages also share a common finger counting method that allows a counter to represent up to one-hundred and forty-four (or 100 in duodecimal) on their two hands.
Using the thumb, the Beoǧǧen speaker counts off each phalange of the four fingers of the right hand to count to twelve, starting with the lowest phalange of the index finger, moving up to the second then third, then likewise the middle, ring finger, and little finger, finishing on the last phalange (or finger tip) of the little finger. This twelve is also marked on the left hand, starting on first phalange of the little finger. When the counter reaches twenty-four, i.e. the second pass of all their right-hand phalanges, they move their left thumb up to the second phalange of the little finger. One continues in this way until the left-hand index finger-tip is indicated with the thumb. Although, in theory it would be possible to continue up to one-hundred and fifty-six (DD 110), in practice this is never done.



This counting system is the reason Beoǧǧen speakers can be seen to habitually run their thumb across their fingers when counting quickly.
Although in personal counting the exact placement of thumb on finger varies from person to person, when gesturing to others - as is very common in markets, food-stalls and other trading situations - more defined gestures are used. For numbers indicated on the first phalange, (e.g. DD 1, 4, 7, T, 10, 40 etc), the fingers are curled into a loose fist, and the thumb place on the side of the phalange to be indicated. This means for the middle, ring and little finger, the thumb is pushed through the closed fingers. To represent the number four, for example, one would make the ‘fig’ gesture, seen below. It’s not uncommon for fingers not to be completely curled in this gesture, leaving more of a half-open fist.



For second-phalange numbers, the thumb is curled over the top of the phalange, rather than touching the underside of it as is usual for counting. Unused fingers are extended.



Finally, for third-phalange numbers, thumb and finger-tip are brought together to form a circle. Unused fingers are stretched out.



A slightly less common system is also used by tradesmen, port workers and sailors to represent the numbers DD 1, 3, 6, 9 and 10. Here the thumb of the right hand represent one, and the remaining fingers three each. The thumb is always left extended to avoid confusion with the more typical gestures explained above. Non-multiples of 3 can be made by using the left hand thumb or thumb and little finger to add one or two to the right hand number. The order of the fingers is such that even from some distance, it is clear what number is being indicated.





[edit] [top]Measuring

Beoggen measurements were formalised by Lartautian nun Iidoo (Beoǧǧen Itou Coupren). Iidoo was a Lartautian Proselyte from the House of Record Keepers - practically speaking, this made her the Lartautian ambassador to the city state of Tubeoǧ. As a record keeper, Iidoo became particularly enamoured with the advanced book keeping and trade culture of Tubeoǧ, and became fluent in Beoǧǧen as well as the mathematics and banking practices of the city state. Eventually she published a short treatise; Regular Weights and Measures, which fast gained popularity and spread across the whole of the northern gulf region almost immediately. While local variations persisted, all trade and inter-city discussions soon adopted the formalised system. Iidoo attempted to spread her system north to her home Empire, but the system was rejected, relying as it did on base-twelve thinking (Lartau is base-ten). Other works elucidating the accounting and trade-logging systems of Tubeoǧ garnered more success.
Shortly after Iidoo’s untimely death in a boating accident, the de facto leader of Tubeoǧ, Praudyaiř Prugäsn Theik, issued a decree to construct the first Hall of Measures, a council of persons responsible for keeping standards of all measurements. The Hall painstakingly measured out each of Iidoo’s standards and created prototypes. A series of copies were made and distributed to select Tubeoǧ makers and trade houses who were given official licence to produce standardised containers, measures and weights. Eventually licence was granted to other major makers in other city states. Each unit had to bear the Hall seal to be considered standard. Five years after it’s creation, the Hall was rehoused in a new building, the proportions of which were all precisely measured to be in-keeping with the Iidoo system.

Length
Chief among Iidoo’s concerns for length was to base the system on the human form. This was already the case for smaller measures, but ratios between units and ultimate sizes varied fairly widely. Longer distances were the least consistent, despite the growing desire to track them over land and sea trade routes, and for the burgeoning sciences. Iidoo based her system on the most ubiquitous small measure, the thumb. For longer distances she favoured the land-traders measures - the gat, tutoukh, and ckiut. These were the distances a voice would carry, the length of the north-east Tubeoǧ city wall (along which a major trade thoroughfare ran) and the distance a caravan would travel before requiring a break, respectively. The gat and tutoukh seem to have changed relatively little, though judging from literature prior to Iidoo, the rest seems to have been reduced considerably - no doubt to keep the system as regular as possible.



Volume
Liquid volume measures were based on two extant Tubeoǧ systems - the apothecaries measures (up to the iusrä), and mead-makers measures for larger volumes. The phew was in essence a new measure. Phew were common place enough - either metal or glazed earthenware jugs, sometimes stopped with oil-cloth and wood plugs, but their sizes varried wildly. After the general adoption of Iidoo’s system, a new, standardised flagon appeared, called beiphew, agreed-flagon, or more informally Itoun phew, an Iidoo’s flagon.
The ksauxm and iusrä were both already relatively standardised by apothecaries and doctors, and were mostly used in prescriptions of herbal medicines and tinctures.The snaid was also common in medicine, though it’s formal relationship of DD 1000 snaid to one ksauxm was not.
Fnos and gyüfnos were also already extant, but varried between states. Variation remained in actual gyüfnos - the large copper or wooden fermenters used by mead-makers - though the formal trade unit of 3 fnos, along with fnos (wooden barrels) themselves eventual standardised in all industries.



Weight
When Iidoo set about standardising weights and measures, there was already one agreed system - the money-changers weights. These five weights were used in all city states to keep track of the large amounts of trade, and to check for coin trimming and other fraud. They were the tös, söbyikh, söxiǧ and baubyikh, and had been standardised some 30 years earlier by the money lenders guild of Essetum. To these Iidoo added one apothecary weight, the dřeit, which was a very rough measure of dry powders - said to be the amount lifted by pressing one’s finger into pile of powder and scraping it off. She also added four market measures, the gyüswour, raig, trät, and ǧeicp, and one traders measure, the ctäy. And of course all were standardised and related.



Area
Of all measures, area was the least formalised when Iidoo began her work. All the terms Iidoo adopted were already in use, the actual area to which they referred varied not only by state, but by individual landowners too. The English definitions are fairly self explanatory, though it should be noted the generative term for referring to area in Beoǧǧen is nöcark, flat, which is reduced to nöca- in compounds. Also, although the terms homestead and estate have been used for tfasm and freph respectively, it should be noted these are broad translations. Large areas of land under the ownership of one family was rare, with most land commonly owned by villagers. Smaller tfasm were more or less privately owned for personal use. Though all of the new standards had a profound effect on commerce in the Beoǧǧen world and beyond, one of the more notable cases stems from these formal packets of land. After considerable petitioning from commoners, the Flouǧs kingdom switched to an area based, rather than percentage/weight based taxation system. This in effect meant farming taxes were tied to production, and not arbitrary volumes set by the king. The method spread, resulting in a more stable yearly yield available directly to commoners themselves.

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