• LeFrog@discuss.tchncs.de
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    2 months ago

    Wow I never thought about that.

    But it is always like this:

    let there be any base "b"
    That can represent a number by the sum of their positional digits:
    
    number = sum(d_i * b ^ i)
       where i is the position index and d_i is the digit at this position. (note: index starts with 0, from the least digit farthest to the right)
    

    So the (decimal) number 4 in base 4 is then

    1×4¹ + 0×4^0 = 10
    

    And (decimal) number 8 in base 8 is

    1×8¹ + 0×8^0 = 10
    

    And 10 in base 10:

    1×10¹ + 0×10^0 = 10
    
  • Wanderer@lemm.ee
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    2 months ago

    Can we all use base 12?

    It will be a shower if shit for like 50 years but then it will be marginally better for pretty much everyone.

      • frezik@midwest.social
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        2 months ago

        Common denominators. You can divide base 12 into half, thirds, fourths, and sixths and still use integers. I find thirds to be particularly useful, so base 16 is out. Base 60 can do it, but that’s getting unweildly.

        • Aceticon@lemmy.world
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          2 months ago

          There are no common denominators in base 12 that you can’t use in base 84, and the latter also has 7 as a common denominator.

          I, for one, vote for changing our base to 84.

          • reiseno_@lemmy.dbzer0.com
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            2 months ago

            You can do base 12 on fingers! You count each of the 3 segments on each finger and ignore the thumb (you can use it to keep your place), so you can count up to 12 on just one hand! :)

            • frezik@midwest.social
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              2 months ago

              This is why I’m not totally sold on the idea that we use base 10 because we have 10 fingers. There are a lot of ways to count with your fingers. Plus, there are many cultures throughout human history that use something else. Base 10 in modern times might just be a historical quirk.

    • Khrux@ttrpg.network
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      2 months ago

      Some people argue that it would be harder to count on your fingers but we could just surgically give everyone more?

      • Cethin@lemmy.zip
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        2 months ago

        Binary is very good for counting with your fingers. With both hands you can count to 1023. One hand is 31, which is still usually more than you typically need to count. It’s also trivial to do once you know how binary works. It takes very little thought, though potentially the decoding could take a bit depending on your proficiency.

        • Daft_ish@lemmy.world
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          2 months ago

          I made it to 27 on my first attempt, so def messed up somewhere. Also, my fingers don’t want to work that way.

          Doable.

          • Cethin@lemmy.zip
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            2 months ago

            I agree it can feel weird, but first this isn’t how we are used to doing it so it hard to compare, and also normally we want our fingers in very precise positions (probably because it’s easier to show other people). When doing binary I feel it’s easier to ignore precise positions. I just use the half of my finger after the middle knuckle and let my fingers move as they please. We only need to track up or down, so it doesn’t need to be precise.

            Practice helps. I’m not good at it, but I can manage it fine at this point. For sure it’d doable, but I rarely have to count, and when I do I can generally do it in my head fine. I could see myself using it maybe if tracking a large number over a long time, but I don’t see that case ever coming up organically.

      • Wanderer@lemm.ee
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        2 months ago

        There are 12 sections on your fingers (excluding your thumb) you then use your thumb to count to 12 on one hand.

        Two hands can allow you to count to 24. Which is way higher than 10. Base 12 is better!

        • Khrux@ttrpg.network
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          2 months ago

          Bold of you to assume I’d ever remember this counting technique. Hell I’m shocked I remember counting my fingers for base 10…

          • techt@lemmy.world
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            2 months ago

            I like the idea of some numbers being popular hand gestures.

            4 - Fuck you; 17 - Shaka (hang loose); 18 - Metal horns; 19 - “I love you”; 132 - Double fuck you

        • Kuragi2@lemmynsfw.com
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          2 months ago

          To be fair, you should be comparing 2 hands in base 12 to 2 hands in base 10, I. E. 20:24. Still a real difference, but not the 10:24 difference you pointed out.

      • frezik@midwest.social
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        2 months ago

        Billions of years ago, our collective great-great-great-[several million more]-grandparent evolved a fin with a five bone structure. That idiot didn’t know anything about common denominators, and now we’re stuck with this numeric system that can’t divide things into thirds without causing issues.

      • rockerface@lemm.ee
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        2 months ago

        When was the last time you’ve actually needed to count something on your fingers?

      • Wanderer@lemm.ee
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        2 months ago

        Every civilised country on earth uses metric.

        Only the really shitty ones use imperial. Imperial is just stupid (unless you count in base 12 ironically)

    • Nafeon@pawb.social
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      2 months ago

      This would be great. I was researching why we don’t have 10 based clocks and then I saw a video about why a 12 and 60 based system is actually much more convenient and now I would love a ‘dozen based metric system’

    • ted@sh.itjust.works
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      2 months ago

      42* years. Centuries are now 84 years. We are living in the 19th century! I rate this idea 12/12.

    • lowleveldata@programming.dev
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      2 months ago

      50 years? I bet we couldn’t even agree on how to write “11” & “12” on such short notice. (See: date format, encoding, etc)

          • BlueKey@kbin.run
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            2 months ago

            In any Base-x system, one digit goes up to x - 1 (with base > 10 we use alphabet letters), then the next digit (to the left) is incremented.
            So in our normal Base-10 system, you count up from 0 to 9 and then add a digit in the front and reset the other digits to get 10.

            This means, that in every Base-x system ‘10’ equals x.
            So you can make the “There 10 types of people …” with every base as ‘10’ in Base-2 means 2, 3 in Base-3 and so on.

  • Orphie@lemmy.cafe
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    2 months ago
    1. This is why I say “10” is not a number, it just means one big group and zero remainder.
    2. I am a huuuuge proponent of dozenal (base-12)
  • shikogo@pawb.social
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    2 months ago

    The most reliable way to communicate bases would probably be using unary. Now if your alien is using unary, that might not work, but it should for all higher bases.

    • witty_username@feddit.nl
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      2 months ago

      I’m not sure if I fully understand.
      I was thinking, wouldn’t it be easiest to describe the system you use by taking the last number in your first decimum and then saying you increment it with one?
      E.g. for base ten this would be: base 9 + 1
      For binary it would be: base 1 + 1
      For hexadecimal it would be: base F + 1
      Etc.

      • Bassman1805@lemmy.world
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        2 months ago

        But if you’re talking to an alien that uses base 4, they don’t know what you mean by “base 9+1”. Wtf is a 9?