Duodecimal Mystery Cache
Hidden : 8/24/2009
Difficulty:
2 out of 5
Terrain:
1.5 out of 5

Size: Size: micro (micro)

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Geocache Description:

*** Cache is not at the posted coordinates ***

In the 60's a neighbor told me about the Duodecimal Society, he later became the president of the Society. The Society purposed to replace our current base 10 numbering system, with a base 12 system, since many of our measurements are based on groupings of 12.

The number twelve possesses several notable characteristics and properties. It is the smallest number with four non-trivial factors (2, 3, 4, 6). Therefore due to increased factorability, duodecimal representations fit more easily than decimal representation into many common patterns. Of its factors, 2 and 3 are prime, which means the reciprocals of all 3-smooth numbers (such as 2, 3, 4, 6, 8, 9...) have a terminating representation in duodecimal. In particular, the five most elementary fractions (1/2, 1/3, 2/3, 1/4 and 3/4), all have a short terminating representation in duodecimal (0.6, 0.4, 0.8, 0.3 and 0.9, respectively). This all makes it a more onvenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary, octal, and hexadecimal systems.

Languages using duodecimal number systems are uncommon; however, there are some in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Kahugu), the Nimbia dialect of Gwandara; the Chepang language of Nepal and the Mahl language of Minicoy Island in India that are known to use duodecimal numerals. In fiction, J. R. R. Tolkien's Elvish languages used duodecimal.

Units of time in many civilizations are duodecimal. There are twelve months in a year, and twelve European hours in a day or night. Traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches. Furthermore, there are twelve signs of the zodiac.

Being a versatile denominator in fractions may explain why there are 12 inches in an imperial foot, 12 ounces in a troy pound, 12 old British pence in a shilling, 12 items in a dozen, 12 dozens in a gross (12 squared = 144 = 1 gross), 12 gross in a great gross (1728, cube of 12), 24 hours in a day (12 * 2), 12 tones in a musical scale, etc. The Romans used a fraction system based on 12, including the uncia which became both the English words ounce and inch. Prior to going to a decimal currency, Great Britain used a mixed duodecimal-vigesimal currency system (12 pence = 1 shilling, 20 shillings or 240 pence to the pound sterling), and Charlemagne established a monetary system that also had a mixed base of twelve and twenty, the remnants of which persist in many places. Drinks are sold in 6-packs (half a dozen) or 12-packs, at least in part, because of the ease of packing instead of an odd shaped packing if 5 items were packaged together.

The first written article suggesting the use of the duodecimal system was in an 1834 article in the Atlantic Monthly, by F. Emerson Andrews . Over the years the duodecimal idea found various supporters including professors that used it in the classes. It was not until 1944 that the Duodecimal Society was formed in New York with the purpose of proposing a conversion to base 12 for all scientific work. The Society is still in existence, but the name has been changed to the Dozenal Society of America and the Dozenal Society of Great Britain. The word "dozenal" is used instead of "duodecimal" because the latter comes from Latin roots that express twelve in base-ten terminology.

A number of letters have been purposed to represent the digits for ten and eleven. Rather than the symbols 'A' for ten and 'B' for eleven, as used in hexadecimal notation, it has been suggested that a script X and a script E be used; to represent the digits ten and eleven respectively, because, at least on a page of Roman script, these characters were distinct from any existing letters or numerals, yet were readily available in printers' fonts. Script X and E were chosen for the resemblance to the Roman numeral X, and as the first letter of the word "eleven". Another popular notation, introduced by Sir Isaac Pitman, uses a rotated 2 to represent ten and a rotated or horizontally flipped 3 (which again resembles a script E) to represent eleven. This is the convention commonly employed by the Dozenal Society of Great Britain and has the advantage of being easily recognizable as digits because of their resemblance in shape to existing digits. It should be noted that for a number of years, the Dozenal Society of America adopted the convention of using an asterisk * for ten and a hash # for eleven. The reason was symbol * resembles a struck-through X while # resembles a doubly-struck-through 11, and both symbols were already present in telephone dials. However, critics pointed out these symbols do not look anything like digits. Problems with these symbols are evident, most notably that most of them do not fit on most calculator displays (although "E" is used on calculators to indicate an error message). However, 10 and 11 do fit, both within a single digit (11 fits as is, while the 10 has to be tilted sideways, resulting in a character that resembles an O with a macron, o or 0). A and B also fit and are used on calculators for bases higher than ten (although B must be represented as lowercase "b" and as such, 6 must have a bar over it to distinguish the two figures). In 'Little Twelvetoes', American television series Schoolhouse Rock! portrayed an alien child using base-twelve arithmetic, using 'dek', 'el', and 'doh' as names for ten, eleven, and twelve, and Andrews' script-X and script-E for the digit symbols. ("Dek" is from the prefix "deca," "el" being short for "eleven" and "doh" an apparent shortening of "dozen."). To indicate that a factional number is not a decimal, a semi-colon is used instead.

Using Duodecimal notation, the cache is located at:


N29° 36;617 W99° 45;579



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