
Post by Buffoonery on Jul 25, 2015 19:30:47 GMT 8
Let's do a test to compare the common fractions with even bases from 618: (Removing the zero to improve legibility)
 Base 6  Base 8  Base 10  Base 12  Base 14  Base 16  Base 18  1/1  1  1  1  1  1  1  1  3/4  .43  .6  .75  .9  .A7  .C  .D9  2/3  .4  .5252¯  .666¯  .8  .9494¯  .AAA¯  .C  1/2  .3  .4  .5  .6  .7  .8  .9  1/3  .2  .2525¯  .333¯  .4  .4949¯  .555¯  .6  1/4  .13  .2  .25  .3  .37  .4  .49  1/2^{3}  .043  .1  .125  .16  .1A7  .2  .249  1/2^{4}
 .0213  .04  .0625  .09  .0C37  .1  .1249 



Post by fcg710647 on Jul 26, 2015 7:11:58 GMT 8
I think those are correct and only bases 12 and 18 have a chance for them, given that you believe 24 is too high of a base. Base 6 terminates all the fractions but it doesn't have three repeating digits at the end as octodecimal does to compensate for the longer expressions for negative powers of two. The opposite effect occurrs when dividing by a bunch of threes; in dozenal 1/3, 1/9, and so on all end in a 4, although only that single digit stays the same. In octodecimal dividing by threes gives shorter expressions but no consistent digit at the end, just as dozenal has shorter ones for negative powers of 2 but no consistent ending digit.



Post by Buffoonery on Jul 27, 2015 11:36:26 GMT 8
Very good point, base 12 and 18 seem to be the best options, I agree completely. They have the best of both worlds (quarters and thirds). But, I can see both systems being used for different applications of mathematics, simply due to the negative powers. Man, that's fun to think about, come to think of it.



Post by fcg710647 on Jul 27, 2015 12:13:51 GMT 8
I thought large negative powers were just written as they are, such as 1/3^8 being 1/6561 in decimal, if you wrote it in base 9 it would be 0.0001 or 1/10000 so it makes sense to write it as 10^(4) where 10 is 9 when written in nonary. That's a nice scientific notation thing but it's not much better than just 3^(8). As for a big number that's not a perfect power at all, Avogadro's Number is 1.111*10^1X in dozenal (since that 10 is twelve) and it's F.590*10^10 in octodecimal (10 being eighteen). It works the same way as long as you're careful. That octodecimal expression translates to about 15.306*18^18 in decimal.



Post by Buffoonery on Jul 28, 2015 9:44:26 GMT 8
Such a huge number for such a small area of space, it's amazing eh? Avogadro's constant boggles my mind when I think about how big this world is, let alone this universe. Imagine expressing his number without scientific notation, lol.



Post by fcg710647 on Aug 14, 2015 9:42:08 GMT 8
You must be busy... in the meantime, I managed to create symbolism for base 42 (2 * 3 * 7), so 18 (2 * 3 * 3) is certainly not too big, LOL Well, Avogadro's without scientific notation would be F590000000000000000 in octodecimal and 602220000000000000000000 in decimal. What about that crazy base 42? r.HLF * 10^C (10 is fortytwo), or rHLF00000000000 without scientific notation. Somewhat shorter than even the Od. representation. r is eleven, H thirteen, L thirtyseven, C fourteen, and F thirtyone. A little h is thirtyfour. R is thirtytwo. The symbols above 20 are derived from adding 21 to those for 020 so it's not super annoying to remember. The Dozenal Society of America has data (multiplication table included) on trigesimal, so I went to the next base with three prime factors; the number of prime factors has a bigger impact on terminating fractions than what those primes are.
1/2 = 0.a 1/3 = 0.C 1/4 = 0.ta 1/5 = 0.8JnT8JnT8JnT8JnT8.... 1/6 = 0.7 1/7 = 0.6 1/8 = 0.5ta 1/9 = 0.4Z
Welp, mentally keeping track of case sensitivity is still a hinderance; I'll stick with Od. for a versatile and efficient system. It's funny how you keep comparing dozenal to decimal when discussing this stuff with me when I do think decimal is pretty boring already.



Post by Buffoonery on Aug 15, 2015 11:44:25 GMT 8
Yeah, finally back. BASE 42! Whaaaaaat lol. Now I'm curious on what your numbers would be. Lol, now I know why the answer to life is 42. You're awesome, that seems like a lot of work, but it's fun to see it in action. My reasoning for comparing to the decimal system is because it's the norm. But, I agree, I'll start comparing to reasonable bases instead, you've got a very good point.



Post by Buffoonery on Aug 15, 2015 12:00:58 GMT 8
About my blog website, I'm comparing it to the decimal system because the site is for people who want to learn how to use the dozenal system. Since we all use the decimal system, it's a way to show them a base that also has relevance to our society. It's already partially included in everyday products. I'll be sure to include a base comparison page though. In fact, I think I'll work on that a bit today, though it probably wont be published today.



Post by fcg710647 on Aug 15, 2015 13:30:40 GMT 8
Yes, when introducing any system to the public, decimal is expected to be the main bearing (control experiment).
Pi in base 42.... 3.5YRHUCrN25rjye6v.... lollol



Post by fcg710647 on Aug 15, 2015 13:51:23 GMT 8
1/4 of 10 (fortytwo) is t.a 1/3 of fortytwo (10) is C Sum, C + t.a = E.a Half of 10 is a (twentyone), E.a * a = U.ta * 10 = Ut.a(Dqg.) Dqg. is the abbreviation for duoquadragesimal lol 0.186A35186A35186A35...(doz.) = 0.6(Dqg.) 0.y(Dqg.) = 0.5186A35186A35...(doz.) = 0.7UA7UA7UA7UA7UA...(Od.), slightly less ugly in octodecimal lmfao



Post by fcg710647 on Aug 15, 2015 13:59:28 GMT 8
Oh, dividing units into 42 on a ruler or a huge pizza? Divide by 2 and then 3.... and then how the hell do you divide by seven?!? Estimate splitting the section such that one portion is 3/4 as large as the other (an offset from halfway). Then divide the larger piece in two; divide the smaller part so that its larger section matches the size of each larger half of the section of four. Then you have three larger bits to divide in two.
A_______________________G A_________B_____________G A_________B______C______G // Then divide segment AB so that one part of it is the same length as those of BC and CG A__D______B______C______G // Now three parts to cut in half. A__D__E___B___F__C__H___G // Yup, divided by seven... although I didn't pick a multiple of seven for the length of AG so it might look ugly.



Post by Buffoonery on Aug 15, 2015 19:30:06 GMT 8
LOL, imagine if another planet used base 42. Haha, father: "now son, you must learn your times tables before you can play video games." son: "but dad, that'll take hours," father: "I know, but we all have to go through with this." son: "I hate math." father: "If only there was a better way to teach you."



Post by Buffoonery on Aug 15, 2015 19:36:26 GMT 8
So what would you call your 8 new symbols? Would you also make modifications to any of the 09? For example, in the dozenal system, "dec" and "elv" make the 2 extra. I've also chosen to say, "sept" instead of "seven" "naught" instead of "zero" "do" instead of "ten" (that last one is crucial) I'm curious now, would you say, "da, de, do, du, za, ze zo, zu" or something?



Post by fcg710647 on Aug 16, 2015 16:53:27 GMT 8
Dr. James Grime says "doh" or "do" for twelve... another problem is the prefix "dodec" such as dodecagon and dodecahedron, where it's two and ten, so "do" stands for two ):
C * 9 in base 42... C is fourteen (1/3 of fortytwo); C * 9 = 10 * 3 = 30 Decimal: 14 * 9... 4 * 9 is 36 because I memorized that ha ha; 90 + 36 = 126 C * 9 in Od... 9 is half of 10 so it's 10 * 7 = 70 I forgot to do base 42's data for its zeroending fractions, such as 60 and 40 being 1/2 and 1/3 in doz. with your colored square charts.... again, the listing is {composite reducers, prime reducers, totatives} Old results: Senary: 0, 3, 0 Decimal: 0, 5, 2 Dozenal: 3, 4, 2 Octodecimal: 3, 8, 4 Vigesimal: 5, 6, 6
Duoquadragesimal: 9, 20, 10 // Whoa (decimal numbers)



Post by Buffoonery on Aug 30, 2015 11:01:47 GMT 8
Hey, very good point. I knew there was a problem when I first found out the name for the base 12 system. The problem is that since they base the name off of our base 10 system, saying "2+10" when you say, "duo decimal"/"do zen". Now, I've seen others try and use the other half of this "dozen," using "zen" to signify '10'. It really frustrates me to attach it like that saying either "do" or "zen" since they are both numbers already unique to themselves. When I was developing my unique nomenclature for 100, 1,000, and 1,000,000 etc. I was always bothered by the whole: Do, gro, mo, bimo, trimo, etc. deal. The reason was Do, gro, and mo, the all sound the same, I want something different, so I made up Gra(Graw) and Meh (may). But, all the while I've been ignoring the very important and fundamental problem from the start. I have to make a new word for '10' then build up from there. Its etymology can't trace back to "two and ten", it has to mean something more rooted and unique. It has to be: 1 syllable (one, two, three...) easy to pronounce (two: 'too') distinguishable from the others (wan, too, three, fower) easily conjoining (Laone, Latwo, Lathree) (not Thraone, Thratwo, Thrathree) It's something I'll have to work on, being careless and just labelling it "Do" would definitely cause problems down the road. One of the first thoughts that came to my head was something like, "Vul" short for vulgar (common/ordinary) or vulgah (division/group) www.etymonline.com/index.php?term=vulgarit also sounds like "full" as in, it's a complete set. But, I don't know, it's something I'd have to really think about. If you have any ideas, I'm all ears. Haha, it's a bit like Lord of the Rings and his Elvish, Orcish, Dwarvish and other cultures Tolkien put in there, it's so much more exciting when you refine something that was only brushed over by many. To put it all into one compact realm, to see them all interact in his saga, it's really something. His representation of these races defined what we think of them nowadays. So if I am to have any say in it, it's gotta be done right, non of this double or even triple syllable nonsense like in hundred or million, and the mix up in the teens (eleven, twelve, thirteen, fourteen, ... nineteen, twenty ???).

