20010704
Basics
Time - Linear Measure - Weight - Derived Units
Duodecimal has found its way into several aspects of language. Early English had a duodecimal counting system - which is why the "teens" start at thirteen, and eleven and twelve have non-derived names. Then there is the dozen itself - and twelve inches in a foot. The metric system would be useful, since it is standardized. Unfortunately, it is based on decimal. A standard metric system based on twelve would offer many more conveniences.
Ten is factorable only by 2 and 5. One third is a repeating decimal; so is a sixth and a ninth, and a twelvth. With duodecimal, these fractions not only no longer repeat, but in other cases, non-repeating decimals are simplified. The only fractions that are simpler in decimal are 1/5 and 1/10 and their higher numerations.
Below is a table of all the fractions of all denominators between 2 and 12 for both decimal and duodecimal systems; underlined numbers are repeating sequences. After that is the multiplication table. One interesting note is that the multiplication tables used in schools is a twelve-by-twelve grid; this shows it takes no great effort to memorize a duodecimal multiplication table.
The number sequence goes like this: 1 2 3 4 5 6 7 8 9 A B 10
^{n}/_{d----} | B_{10 } | B_{12 } | ------ | ^{n}/_{d----} | B_{10 } | B_{12 } | ------ | ^{n}/_{d----} | B_{10 } | B_{12 } |
^{0}/_{1 } | 0 | 0 | - | ^{4}/_{11 } | 0.36 | 0.4 | - | ^{7}/_{10 } | 0.7 | 0.84972 |
^{1}/_{12 } | 0.83 | 0.1 | - | ^{3}/_{8 } | 0.375 | 0.46 | - | ^{5}/_{7 } | 0.714285 | 0.86A351 |
^{1}/_{11 } | 0.09 | 0.1 | - | ^{2}/_{5 } | 0.4 | 0.4972 | - | ^{3}/_{11 } | 0.72 | 0.8 |
^{1}/_{10 } | 0.1 | 0.12497 | - | ^{5}/_{12 } | 0.416 | 0.5 | - | ^{3}/_{4 } | 0.75 | 0.9 |
^{1}/_{9 } | 0.1 | 0.14 | - | ^{3}/_{7 } | 0.428571 | 0.5186A3 | - | ^{7}/_{9 } | 0.7 | 0.94 |
^{1}/_{8 } | 0.125 | 0.16 | - | ^{4}/_{9 } | 0.4 | 0.54 | - | ^{4}/_{5 } | 0.8 | 0.9724 |
^{1}/_{7 } | 0.142857 | 0.186A35 | - | ^{5}/_{11 } | 0.45 | 0.5 | - | ^{9}/_{11 } | 0.81 | 0.9 |
^{1}/_{6 } | 0.16 | 0.2 | - | ^{1}/_{2 } | 0.5 | 0.6 | - | ^{5}/_{6 } | 0.83 | 0.A |
^{2}/_{11 } | 0.18 | 0.2 | - | ^{6}/_{11 } | 0.54 | 0.6 | - | ^{6}/_{7 } | 0.857142 | 0.A35186 |
^{1}/_{5 } | 0.2 | 0.2497 | - | ^{5}/_{9 } | 0.5 | 0.68 | - | ^{7}/_{8 } | 0.875 | 0.A6 |
^{2}/_{9 } | 0.2 | 0.28 | - | ^{4}/_{7 } | 0.571428 | 0.6A3518 | - | ^{8}/_{9 } | 0.8 | 0.A8 |
^{1}/_{4 } | 0.25 | 0.3 | - | ^{7}/_{12 } | 0.583 | 0.7 | - | ^{9}/_{10 } | 0.9 | 0.A9724 |
^{3}/_{11 } | 0.27 | 0.3 | - | ^{3}/_{5 } | 0.6 | 0.7249 | - | ^{10}/_{11 } | 0.90 | 0.A |
^{2}/_{7 } | 0.285714 | 0.35186A | - | ^{5}/_{8 } | 0.625 | 0.76 | - | ^{11}/_{12 } | 0.916 | 0.B |
^{3}/_{10 } | 0.3 | 0.37249 | - | ^{7}/_{11 } | 0.63 | 0.7 | - | ^{1}/_{1 } | 1 | 1 |
^{1}/_{3 } | 0.3 | 0.4 | - | ^{2}/_{3 } | 0.6 | 0.8 | - |
There are six less repeating fractions in duodecimal than decimal; of the twenty-four that do repeat, ten are shorter in duodecimal. As for non-repeating fractions, six are shorter in duodecimal than decimal. Fifths, Sevenths, Tenths, and Elevenths repeat in duodecimal; Thirds, Sixths, Sevenths, Ninths, Elevenths, and Twelvths repeat in decimal.
With the basic mathematics set out, the duodecimal system of weights and measures is presented below.
Sym Term Length in Seconds Costumary Length uC microchron 1 1 1 s 12 12 12 s 12^2 144 2 m 24 s mC millichron 12^3 1 728 28 m 48 s cC centichron 12^4 20 736 5 h 45 m 36 s dC decichron 12^5 248 832 2 d 21 h 7 m 12 s C Chron 12^6 2 985 984 34 d 13 h 26 m 24 s DC Dekachron 12^7 35 831 808 1 y 49 d 17 h 16 m 48 s HC Hectochron 12^8 429 981 696 13 y 231 d 15 h 21 m 36 s KC Kilochron 12^9 5 159 780 352 163 y 224 d 16 h 19 m 12 s 12^10 61 917 364 224 1 963 y 141 d 3 h 50 m 24 s 12^11 743 008 370 688 23 560 y 233 d 22 h 4 m 48 s MC Megachron 12^12 8 916 100 448 256 282 727 y 252 d 0 h 57 m 36 s |
Don't forget that what you are seeing above is actually the decimal conversion of duodecimal numbers. For example, 12^{3} -- 1,728 -- is 1,000 in base 12. Also, the units of time divide evenly into eachother -- there are 144 (100 b12) seconds in a minute, 12 (10 b12) minutes in a period, 12 (10 b12) periods in a shift, 4 shifts in a day or 12 (10 b12) shifts in a week, 12 (10 b12) weeks or 36 (30 b12) days in a month, and 12 (10 b12) months in a year. Not only do the duodecimal times come comfortably close to those natural to humans and most other earth life, but it is also a repeating pattern of 12 or some order thereof going up to the next level, unlike the 60-60-24-7-4-12/365-1 rate of the currently used system. This allows a much easier transition from days to minutes or months to days (for example -- using our current method of measuring time, how many days are there in 5 months? Hmm? Which months, you ask? You wouldn't be asking that if you were using my time system).
Earth is the only planet that has 86459 seconds or so to a day (well, Mars comes close), and about 31557600 seconds in a year (with no editing for day/light cycle; the "day" your watch uses is 86400 seconds long, and the non-leap "year" is 31536000 seconds long). The Earth's rotation and revolution are not constants themselves. Earth is slowly slowing its spinning (thanks to the tides of the Sun and the Moon), and the orbit around the sun is subject to gravitational perturbances from Jupiter and the other planets.
We use a tortured system of 60 seconds to a minute; 60 minutes to an hour; 24 hours to a day; 7 days to a week and 28, 29, 30, or 31 days to a month; and twelve months of differing sizes to a year that is six hours short of Real Time, so we add an extra day every four years to make up for it except for every 100th year. The daily cycle starts in the middle of the night, making us say non-sensical things like it being "in the morning" when sunrise is still six hours away.
With a possible destiny for Humanity in space, Earth's rate of rotation and lunar cycles and time of revolution would be completely irrelevant. It would be better to use a universal time measurement system - the only other option is fragmentation by use of local systems that would cause all sorts of translation headaches.
Sym Term Metric Equal U.S. Garbage Measure uL microlin 12^-6 0.019458 um mL millilin 12^-3 33.623719 um cL centilin 12^-2 0.403485 mm dL decilin 12^-1 4.841816 mm (3/16 of an inch) L Lin 1 5.810178 cm (2.2875 inches) DL Dekalin 12 69.722144 cm (2' 3.450") HL Hectolin 12^2 8.366657 m (27' 5.396") KL Kilolin 12^3 100.399888 m (329' 4.751") ML Megalin 12^6 173.491006 km (107 miles 4236' 2.558") |
The next measures are added for reference; the first is important because it is exactly one light-second long; the third is the Light-Chron or Photochron (symbol P). The other two units offer intermediate and large scale units
GL Gigalin 12^9 299 792.458 km (186 282 miles 2100 feet - a light-second) TL Teralin 12^12 5.18041x10^8 km (~3.465 AU) PL Petalin 12^15 8.9517x10^11 km (~0.095 light-years or ~6 000 AU) EL Exalin 12^18 1.5469x10^15 km (~164 light-years) |
Sym Term Metric Equal U.S. Measure uM micromass 12^-6 65.6872362 ug mM millimass 12^-3 113.5075441 mg cM centimass 12^-2 1.3620905 g dM decimass 12^-1 16.3450864 g (~0.58 oz) M mass 1 196.1410363 g (~6.92 oz) DM Dekamass 12 2.3536924 kg (~5 lbs 3 oz) HM Hectomass 12^2 28.2443092 kg (~62 lbs 4 oz) KM Kilomass 12^3 338.9317111 kg (~747 lbs 3 oz) MM Megamass 12^6 585 673.996 kg (~645 tons 1190 lbs 2 oz) |
The "Vol", one cubic lin (one mass is one cubic lin of water).
Density
The "Den". One Mass per Vol - represented as a ratio to the density of pure water at the triple point (unity). For example, in decimal metric, Iron has a specific gravity (density, ratio to water) of 7.86 (grams per cubic centimeter). Iron is 1541 dens (1541 masses per cubic lin); or, to put it in duodecimal, a85 dens.