Dozenal (or Duodecimal) System

Discussion in 'General discussion' started by Gabachi, May 14, 2013.

  1. Gabachi

    Gabachi The Most Unjunior Member

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    People are trying to change how we count. This is a small minority, however, I found it very interesting and actually played with many numbers and even greek symbols.

    Now normally we count
    1 2 3 4 5 6 7 8 9 10
    right?

    Our entire system is based on ten. However, the main problem with that is,
    10/3=0.3333333333333333333333333333333333333333333333333333333333333.....
    10/4=2.5
    10/6=1.6666666666666666666666666666666666666666666666666.....

    We bump into major problems with dividing thirds, fourths, and sixths. Now this new system is based on 12. Ten is only divisible by 2, 5, and itself. Twelve is divisible by 2, 3, 4, 6, and itself. Five actually get turned into the infinite decimal number.

    Now how do you count in base 12?
    1 2 3 4 5 6 7 8 9 X ε 10

    X - dec or dek (derived from Latin, equivalent to the decimal 10)
    ε - el (short for eleven, equivalent to the decimal 11)
    10 - doe (short for dozen, equivalent to the decimal 12)

    Dozenal 20 would be equivalent to the decimal 24 and would be pronounced two doe (two dozen).
    100 would be called a groe (or gross). 300 would be three groe.

    10/2=6
    10/3=4
    10/4=3
    10/6=2

    Now while the naming for numerals like 20 or 400 make a lot of sense, they don't exactly roll off the tongue, nor would they sound similar in other languages. I have devised a system (out of pure boredom) of names mainly because I am fascinated with language. They are based on latin suffixes that we all can identify. I'm not really suggesting we use this system (and it would be difficult to implement anyway considering how widespread metric is)....maybe a little, but it won't happen aha.

    Instead of using an X for decimal 10 which looks quite ugly stuck in the middle of a bunch of numbers, I use the greek letter omega to compliment epsilon for decimal 11. I also converted several astronomical dates and ages to dozenal as well.

    Tell me what you think! Remember this was purely for fun. My sick, twisted version anyway!

    Numbers
    1 - one
    2 - two
    3 - three
    4 - four
    5 - five
    6 - six
    7 - seven
    8 - eight
    9 - nine
    Ω - dek
    ε - el
    10 - doe
    11 - doe one (one dozen one)
    12 - doe two
    13 - doe three
    14 - doe four
    15 - doe five
    16 - doe six
    17 - doe seven
    18 - doe eight
    19 - doe nine
    1Ω - doe dek
    1ε - doe el
    20 - dudoe (two dozen)
    21 - dudoe one
    22 - dudoe two
    30 - trudoe
    40 - quadoe
    50 - quidoe
    60 - sexdoe
    70 - sepdoe
    80 - octdoe
    90 - novdoe
    Ω0 - decdoe
    ε0 - undecdoe
    100 - groe
    200 - dugroe
    300 - trugroe
    400 - quagroe
    500 - quingroe
    600 - sexgroe
    700 - sepgroe
    800 - octgroe
    900 - novgroe
    Ω00 - decgroe
    ε00 - undecgroe
    1000 - gran (from great gross or grand gross)
    2000 - dugran
    3000 - trugran
    4000 - quagran
    5000 - quigran
    6000 - sexgran
    7000 - sepgran
    8000 - octgran
    9000 - novgran
    Ω000 - decgran
    ε000 - undecgran
    10,000 - doe gran
    40,000 - quadoe gran
    28,Ω91 - dudoe eight gran, decgroe novdoe one
    1,000,000 - milgroe
    1,000,000,000 - gran milgroe
    1,000,000,000,000 - bilgroe

    Age of Celestial bodies
    Ω68 milgroe years - age of the earth
    Ω75 milgroe years - age of the solar system
    2.81 gran milgroe years - age of the universe
    3.42 milgroe years - lifespan of a Type-O star
    29.6 milgroe years - lifespan of a Type-A star
    23Ω milgroe years - lifespan of a Type-F star
    1.ε3 gran milgroe years - lifespan of a Type-G star (sun)
    4.Ω2 gran milgroe years - lifespan of a Type-K star

    Orbital Periods of Celestial Bodies
    74 days - orbital period of Mercury
    169 days - orbital period of Venus
    256 days - orbital period of Earth
    23 days - orbital period of the Moon
    493 days - orbital period of Mars
    10 years - orbital period of Jupiter
    25 years - orbital period of Saturn
    70 years - orbital period of Uranus
    119 years - orbital period of Neptune
    188 years - orbital period of Pluto
    6720 years - orbital period of Sedna

    Now the omega looks a little weird but is better by far than the X. If there's any other numbers you would like, just ask! I can also do dates as well.

    Something else interesting to note is that we are approaching the dawn of the 13th dozenal "century" (which last 144 years each).

    Today is May 11th, 11ε9.
     
    #1 Gabachi, May 14, 2013
    Last edited: May 14, 2013
  2. NotWhatWeExpected

    NotWhatWeExpected Today is tomorrow New Zealand
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    While a base 12 system would be much helpful, the levels of confusion would be devastating. There's no way I'm going back to elementary school math to learn a new system.

    If you end up with a .66666666666666666666, just use 2/3 instead. It's much cleaner and everyone still knows what it means.

    Also: Using X as a character (even if it looks slightly different by Greek terms) would be a VERY bad idea, as that would screw over every function ever.
     
    #2 NotWhatWeExpected, May 14, 2013
    Last edited: May 14, 2013
  3. Keldeo

    Keldeo Am I really well-known though

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    Creative solution to a simple math problem, lol. But I don't see why anyone would actually consider it practical to change from the base 10 system everyone is used to. I mean, it's been used since ancient times, because it's intuitive. It's how many fingers we have. XD

    Systems like this have been devised for other purposes though. The programmers around here can attest to it; ever heard of hexadecimal? It's exactly this, except based on sixteen instead of twelve.

    1 = 1
    2 = 2
    [...]
    9 = 9
    10 = A
    11 = B
    12 = C
    13 = D
    14 = E
    15 = F
    16 = 10

    It's why we see numbers like "0xFF0000" on the net all the time.

    The hexadecimal system was devised to make binary easy to read (unless you're a robot or something, the number 0100010111011010 probably looks near unreadable or at least a pain in the ass). But in hex every four binary digits is represented by a single numeral, so binary "0100 0101 1101 1010" becomes "0x45DA" which is much easier for a human to read and remember. It's also where programmers get numbers like 65,535 and 8192 from--those numbers might look arbitrary to an ordinary person, but in hex, they're the nice round values "0xFFFF" and "0x2000". Numbers like those will pack well into memory, so they make CPU caching faster and more efficient.

    ...but programmer talk aside.

    I've actually done something like this, myself. Using what I knew about alternate number systems (having learned that the decimal system was more or less arbitrary), I created a calendar for the fantasy setting I run my D&D games in... and you guessed it, it's based on twelves. I started by giving each month a name just like we do in the real world, but I also gave each year a name. So both the months and years in the setting are both counted in cycles of twelve. The "First Year of Birth Sun" would be the year 0, followed by the First Year of Rising Sun, First Year of Bright Sun, etc, all the way out to the First Year of Last Sun, which would be year 11. After that it loops around to Second Year of Birth Sun for year 12, Second Year of Rising Sun for year 13, and so on. So when the calendar says something like "121st Year of Birth Sun", it's the first year of the 121st twelve-year cycle, which would be year 1452 if they were counted consecutively from zero.

    Additionally some characters believe that good luck comes during months that share a name with the year they're in, such as the month of Birthmoon during a Year of Birth Sun, or Risingmoon during a Year of Rising Sun. They might go around boasting about how they were born in such a month and so they're superior somehow, for example, or a superstitious village might consider a wanderer showing up on those dates to be a good omen.

    'Course, just like you I did this solely for fun, not because I thought it was practical, rofl. It was just to make the setting feel richer.
     
  4. Sparkypony

    Sparkypony Antisocial ponyality disorder

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    Do you know how much this would screw up all computer systems in the world?
     
  5. Yamiookami

    Yamiookami EP's Resident Yami

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    You mean the computer systems that run on binary, which is itself a different counting system?

    Sent from my DROID3 using Tapatalk 2
     
  6. Sparkypony

    Sparkypony Antisocial ponyality disorder

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    It'd break the calculators. I know that much.

    And nearly all of the math formulas in recent history would have to be re-done. Its impractical unless you're gonna use it for a specific computer system.
     
  7. mike406

    mike406 Moderator
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    I honestly don't see this happening. It's completely impractical. And recognizing standard fractions to their decimal form should be easy for most people.
     
  8. Sparkypony

    Sparkypony Antisocial ponyality disorder

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    Some people are pretty stupid...

    Anyway, yeah. No real point here unless you're gonna build a hardware system that uses this base 12.

    Why is there no base 20?
     
  9. Keldeo

    Keldeo Am I really well-known though

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    There is. The Mayans used it. lol
     
  10. Yamiookami

    Yamiookami EP's Resident Yami

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  11. Ash243x

    Ash243x A Pony Every Pony Should Know
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    Many people have proposed 12 as a "better" number for counting... and if we had not been using base 10 for centuries already then maybe that would have been a good idea... but we have been and so changing now would never happen or even make much sense. Base-12 supporters will have to be satisfied with having already won the Time-Keeping standards war; of which I am already endlessly annoyed (If it were up to me, everyhting would be base 10, including clocks)
     
  12. Sparkypony

    Sparkypony Antisocial ponyality disorder

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    If we had used base ten for clocks i don't think it'd change.

    Personally i'd change it to where each minute has a hundred seconds. And so on.
     
  13. Keldeo

    Keldeo Am I really well-known though

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    I don't know about any thirties, but I know the Babylonians worked with base 60. It's the reason we have 60 seconds in a minute and 60 minutes in an hour. Similarly to how the dozenists argue that 12 has more factors than 10, I think the Babylonians chose 60 because it's got all the factors of 12 and then some. Plus it fits neatly into the math of dividing a day into 24 hours.

    ...the hell?
     
  14. Ash243x

    Ash243x A Pony Every Pony Should Know
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    The French had a beautiful decimalization plan at the time they were inventing and implementing the Metric System for science units. A day consisted of 10 hours, each having 100 minutes, and each minute having 100 seconds. A week would be exactly 10 days long, and a month was always exactly 3 weeks (30 days). There would still be 12 months, but now they are all perfectly equal, and any leftover days (5 or 6 depending on if it's a leap year) are just a national vacation or something.
     
  15. Sparkypony

    Sparkypony Antisocial ponyality disorder

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    Ok now it makes sense. I'm not really good at math. I know enough to use a calculator though.

    Should have done that instead.
     
  16. Ash243x

    Ash243x A Pony Every Pony Should Know
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    I really wish it had caught on :/
    It would make telling time way easier in base-10 units, and even more, it would mean you could re-use calendars every year because they would all be the same, instead of having what we do now, where the 7-day week is completely out of sync with a 365 day year.

    Meanwhile, the US hasn't even gotten it's act together enough to adopt Metric for anything at all, let alone time
     
  17. Sparkypony

    Sparkypony Antisocial ponyality disorder

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    Imperial works just fine for me.
     
  18. Keldeo

    Keldeo Am I really well-known though

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    Honestly I don't think I could get used to a base 10 timekeeping system, lol. Dates I could probably deal with because it's not that different from how we already do things (the Babylonians invented the 360-day year, which is also why we divide circles into 360 degrees. Fun fact). But base 10 for time... I dunno. I guess I'm just too used to the 60's and 24's the Babylonians gave us. :(

    I guess when you're an ancient civilization who invents a working mathematical system, it doesn't really matter if a new one is devised 4000 years later. People will still stick to yours just because it was the first. XD
     
  19. Yamiookami

    Yamiookami EP's Resident Yami

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    It's a hexidecimal pun.
     
  20. mike406

    mike406 Moderator
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    I agree, I think the current time system works just fine. And it'd certainly take some time accustoming ourselves to what the "new" minute would "feel like".
     

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