
Vreleksá The Alurhsa Word for Constructed: Creativity in both scripts and languages

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Kiri
Joined: 13 Jun 2009 Posts: 471 Location: Latvia/Italy

Posted: Thu Aug 27, 2009 11:02 pm Post subject: Numeric Systems, oppinion needed. 


Hey everyone! Wasn't sure, if I could post this under Conlangs, so posted it here. It's a bit mathematical, but it's nothing too extraordinary
Let's see, if I am able to explain my thoughts.
I was thinking numbers in a highly linguistic way. So I'm gonna use terms like "the linguistic equivalent of [number]. Please don't be disturbed by that. So, here I go.
Here on Earth we are used to a decimal numeric system. We have separate words for 1 to 10 (or to 12, as in English), that are unique, but after that they are all variations of those numbers. For example, in Latvian, četrpadsmit (14) is formed of četripāridesmit (4over10), but the "round" četrdesmit (40) is formed of četri(reiz)desmit (4(times)10). The next unique number is 100, which is 10x10, and after that  100=10x10x10.
And then, in measures, 100 centimeters equal 1 meter, 1000 meters equal 1 kilometer and so on. I hope you get my drift.
Of course, we also use a sixbased numeric system, when counting time. There are 60 seconds in a minute, 60 minutes in an hour and 24 hours in a day  all of these numbers divide with six, therefore it's a sixbased numeric system.
So, on to the point.
In a world, where the dominating race is someone besides human, isn't it quite likely to have a different numeric system, in a linguistic way? For example, they would have a system that's based on, let's say, fourteen.
They would have unique words for numbers one to fourteen. 15 would be 14+1. 16 would be 14+2 and so on. The linguistic equivalent of 20 would be 2x14=28. instead of 30, 40, 50, 60, 70, 80 and 90 they would use 42, 56, 70, 84, 98, 112 and 126 as "round" numbers. They would take this even further, because they would consider numbers like 10x14=140, 11x14=154, 12x14=168 and 13x14=182 "round". Although they look absolutely horrible to me, these would be normal "round" numbers for them. The linguistic equivalent of 100, therefore having it's own unique name would be 14x14=196. (This is already making my head spin, but I will continue anyway). The roundness of 200 would be possessed by a number as horrible as 392. And the linguistic equivalent of the nice 1000 would be 14x14x14=2744...
On to the forming of decimal round numbers in this system.
20=14+6
30=28+2=2x14+2
40=28+12=2x14+2
50=42+8=3x14+8
60=56+4=4x14+4
70=70(+0)=5x14(+0)
80=70+10=5x14+10
90=84+6=6x14+6
100=98+2=7x14+2
110=98+12=7x14+12
120=112+8=8x14+8
130=126+4=9x14+4
140=140(+0)=10x14(+0)
150=140+10=10x14+10
... I'm looking at these numbers filled with ultimate crazyness. But I managed to see a sequence of the added numbers: 621284010. Based on this, I believe, there is a formula possible for easy(er) transcription from decimal numbers. Otherwise it's a mathematical madness. But a fascinating one, don't you think?
... or is it just me being insane? 

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Tolkien_Freak
Joined: 26 Jul 2007 Posts: 1231 Location: in front of my computer. always.

Posted: Fri Aug 28, 2009 1:17 am Post subject: 


It is an interesting madness. I can't speak at all to easy conversion (I'm sure it's possible), but still.
Different bases are always fun  I believe I've mentioned several times Emitare's use of base 8. (So it goes 1 2 3 4 5 6 7 10 11...) 

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Aert
Joined: 03 Jul 2008 Posts: 354

Posted: Fri Aug 28, 2009 1:37 am Post subject: 


got it!
x*14+n > n is from a base14 system as well, the n just decreases by 4 each time the x increases, in a modular fashion around 14 (like a clock).
30=1*14+(4*4)
40=2*14+(4*3)
50=3*14+(4*2)
60=4*14+(4*1)
70=5*14+(4*0)
80=6*14+(4*1)
the problem is since you're using a second base larger than the first, you'll get negative numbers.
the sequence you're seeing is the modular rhythm around 14, subtracting 4 each time: 4>0>(144)=10>6>2>(14(42))=12>8>4, etc
I don't know if that helps you at all, but good luck with your numbers system
Mine is base 25 (one of the weirdest, but I kind of like it  considering going to 24 though) 

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Kiri
Joined: 13 Jun 2009 Posts: 471 Location: Latvia/Italy

Posted: Fri Aug 28, 2009 9:10 am Post subject: 


Ak šausmas, Mathematics in English is quite challenging
But
90=6x14+6, where 6 isn't really 4xanything
100=7x14+2, and 2=4x0.5
.. or did I misunderstand you?
Anyways, thank you very much for helping me! 

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Aert
Joined: 03 Jul 2008 Posts: 354

Posted: Fri Aug 28, 2009 3:06 pm Post subject: 


The +6 is part of the mod14 set I mentioned earlier (the 6212840106).
If you swapped the bases you wouldn't have the problem of + negativen*4 later on, or did something else, I don't know  this system looks a bit complex or something to use as a simple number system, unless you can find a way to make it work. 

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Kiri
Joined: 13 Jun 2009 Posts: 471 Location: Latvia/Italy

Posted: Fri Aug 28, 2009 7:05 pm Post subject: 


Well, yeah, the 14 was just an example. I am definitely using a nondecimal numeric system, but I should probably settle with something more comparable
Thanks! 

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eldin raigmore Admin
Joined: 03 May 2007 Posts: 1621 Location: SouthEast Michigan

Posted: Sat Jul 16, 2016 12:37 am Post subject: 


Have any of us ever used a numeralbasesystem in one of our conlangs, in which none of:
{two; three; four; five; six; seven; eight; nine; ten; twelve; fourteen; fifteen; sixteen; eighteen; twenty}
was one of the bases?
Have any of us ever used a base smaller than four?
Have any of us ever used an odd base (other than five)?
Have any of us ever used a basesystem in which the smallest base was greater than twenty? (I think the answer is yes; I think someone used base twentyfive and someone used base thirty.)
Do any of us prefer bases which are powers of primes? (e.g. four, eight, sixteen; or nine)
Or, primes themselves? (e.g. five, seven)
How common are bases divisible by neither three nor five? (like two, four, seven, eight, fourteen, sixteen)
How popular are bases divisible by a prime over ten, such as multiples of eleven, or of thirteen, or of seventeen, or of nineteen? _________________ "We're the healthiest horse in the glue factory"  Erskine Bowles, CoChairman of the deficit reduction commission 

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