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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 četri-pāri-desmit (4-over-10), 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 six-based 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 six-based 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: 6-2-12-8-4-0-10. 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?   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...)   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 base-14 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->(14-4)=10->6->2->(14-(4-2))=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)   Kiri Joined: 13 Jun 2009
Posts: 471
Location: Latvia/Italy Posted: Fri Aug 28, 2009 9:10 am    Post subject: Ak ausmas, Mathematics in English is quite challenging But 90=6x14+6, where 6 isn't really 4x-anything 100=7x14+2, and 2=4x0.5 .. or did I misunderstand you? Anyways, thank you very much for helping me!    Aert

Joined: 03 Jul 2008
Posts: 354 Posted: Fri Aug 28, 2009 3:06 pm    Post subject: The +6 is part of the mod-14 set I mentioned earlier (the 6-2-12-8-4-0-10-6). If you swapped the bases you wouldn't have the problem of + negative-n*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.   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 non-decimal numeric system, but I should probably settle with something more comparable Thanks!   eldin raigmore 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 numeral-base-system 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 base-system in which the smallest base was greater than twenty? (I think the answer is yes; I think someone used base twenty-five 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, Co-Chairman of the deficit reduction commission   Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
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