
Post by Buffoonery on Jul 25, 2015 19:56:31 GMT 8
These are the powers of 2 expressed in even bases 618:
 Base 6  Base 8  Base 10  Base 12  Base 14  Base 16  Base 18  2^{1}  2  2  2  2  2  2  2  2^{2}
 4  4  4  4  4  4  4  2^{3}  12  10  8  8  8  8  8  2^{4}  24  20  16  14  12  10  G  2^{5}  52  40  32  28  24  20  1E  2^{6}  144  100  64  54  48  40  3A  2^{7}  332  200  128  A8  92  80  72  2^{8}  1104  400  256  194  144  100  E4  2^{9}  2212  1000  512  368  288  200  1A8 
1/n ^{1 }+ 1/n ^{2} + 1/n ^{3}...
 Base 6  Base 8  Base 10  Base 12  Base 14  Base 16  Base 18  1/2^{1}  .3  .4  .5  .6  .7  .8  .9  1/2^{2}  .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  1/2^{5}  .01043  .02  .03125  .046  .061A7  .08  .0A249  1/2^{6}  .0003213  .01  .015625  .023  .030C37  .04  .051249  1/2^{7}  .0014043  .004  .0078125  .0116  .01761A7  .02  .029A249  1/2^{8}  .00050213  .002  .00390625  .0069  .00AA0C37  .01  .014E1249  1/2^{9}  .000231043  .001  .001953125  .00346  .0055061A7  .008  .00B70A249 



Post by on Sept 13, 2015 20:00:33 GMT 8
Let's do 'em for quadrivigesimal and alphadecimal... Power__Base 24__Base 36
2^4______J_________J 2^5______18________R 2^6______2J________1Z 2^7______58________3P 2^8______tJ________74 2^9______a8________C8
Fractions?
1/2______0.U_______0.y 1/4______0.6_______0.9 1/8______0.3_______0.4y 1/2^4____0.1U______0.29 1/2^5____0.0y______0.14y 1/2^6____0.09______0.0P9 1/2^7____0.04U_____0.0t4y 1/2^8____0.026_____0.0529
36 is looking better for the fractions but not the integers. Choosing the best base is pretty tough, lol



Post by Buffoonery on Sept 17, 2015 17:56:37 GMT 8
Wow, that's very impressive, look at that! Man, I really like how clean it is. Oh well, base 12 also looks pretty good considering it's such a low base. It still can't compete against base 16 though for powers of 2.



Post by on Sept 18, 2015 14:45:25 GMT 8
Fraction______Trigesimal______Duoquadragesimal (Sievenal) 1/2_______________0.A_______________0.a 1/4_______________0.7A______________0.ta 1/8_______________0.3]A_____________0.5ta // That one is uglier using thirty, only the A stays the same. 1/2^4_____________0.1?7A____________0.2?ta // That "ta" holds on for fortytwo, and the ? is an even digit so the next step is pretty easy. 1/2^5_____________0.0Z3]A___________0.1H5ta // The trigesimal endings are alternating between 3]A and ?7A.... uglier than fortytwo's 5ta and ?ta. 1/2^6_____________0.0C1?7A__________0.0nj?ta // That one is pretty much a draw, other than the ending digit feature again. At least the ? and t are both even.
Other common fractions in sievenal?
1/3 = 0.C 2/3 = 0.Z 3/4 = 0.Fa 1/6 = 0.7 5/6 = 0.D // Those are nice.
1/9 = 0.4Z 2/9 = 0.9C 5/8 = 0.5ta + 0.a = 0.?ta // Good coincidence, the other ending three digits when dividing 1 by a bunch of twos, like 5/8 in decimal being 0.625 and one sixteenth being 0.0625, nice to remember. 1/7 = 0.6 // O.o now we can get averages per day if we are given an amount per week via dividing by seven. Did we get seven days in a week from dividing lunar cycles by four? 2/7 = 0.U 3/7 = 0.y 1/C = 0.3 // C is fourteen
Oh, I forgot all important twelfths; the ones that don't reduce are one, five, seven, and eleven twelfths.
1/U = 0.3a 5/U = 1/3 + 1/U = 0.C + 0.3a = 0.Na 7/U = 1/U + 1/2 = 0.3a + 0.a = 0.Ea r/U = 5/U + 0.a = 0.wa // Maybe you don't like having twodigit stuff there, but 0.wa becomes 0.9166666666.... in decimal, I am pretty much satisfied with the representation not recurring, unless there is ugly behavior like dividing by twos in trigesimal.



Post by Buffoonery on Oct 11, 2015 8:29:48 GMT 8
Base 42 seems to work well with 3's, 6's, and 7's, which I think might be useful for calendars, and dates in general.
 Grr, it's hard to remember what your symbols stand for, especially with the ? and ]. But I guess if there's a story to go with it, it would help with the remembrance.
In Hexidecimal, stating that: 3/4 of 10 = C makes sense because 1 2 3 4 (quarter) 5 6 7 8 (half) 9 A B C (three quarter) D E F 10
It's easy to do in you head since it's only 6 extra symbols that work in a uniform fashion. However when I see that in base 42, Sievenal: 2/7 = 0.U
It seems so weird to me.
1 2 3 4 5 6 7 8 9 t r U //Right here H C A J N y G P b F L v Z w D K m ...            
I got these symbols from a previous post you made, but I'm wondering if there's a way I can remember them. So far, I recognize "t" standing for "ten", but "r", "U", "H"... I'm confused.



Post by on Oct 11, 2015 15:21:18 GMT 8
Which symbol set? The last one I posted was a noncase sensitive one for trigesimal; my symbols for larger bases differ for the numbers 21 through 28. The weird bit is that some symbols are reused in both sets (such as Z and K) but represent different numbers. m is 29 in both cases.



Post by Buffoonery on Oct 11, 2015 15:44:08 GMT 8
I'm just wondering the mindset behind the letter choices. The simplest solution is to say A,B,C,D,...



Post by on Oct 11, 2015 16:03:04 GMT 8
The case sensitivity might tell the fate of 36 and 42; if mentally handling symbols with different numbers for N and n, E and e, H and h, etc. etc. becomes a turd then the highest applicable base would be trigesimal. If it's not harder, 36 and 42 may still have a purpose lol
Dividing 365.2422 days into 42 "pseudo months" would have 29 of these that contain 9 days and 13 that have 8 days a piece.
I still need to know if people would be more compatible with changing to a base that's a multiple of ten because they're so used to decimal (does trigesimal get an advantage here?)



Post by on Oct 11, 2015 16:04:40 GMT 8
Oooooh my bad, you divided 364 into thirteens so that each division would have exactly 4 weeks. That would be nice, although even base 26 would be ugly.



Post by on Oct 13, 2015 18:56:47 GMT 8
6 is the least common multiple of the highly important primes 2 and 3, and the least common multiple of 6 and 7 is already 42. If 7s are more important than 5s (maybe due to the weekly cycle), then 42 trumps 30. In base 36, 10  1 days would give 5 weeks, but then you have to do 30  3 for fifteen weeks, etc. In base 42, 10 days = 6 weeks = 3 fortnights.



Post by Buffoonery on Jan 14, 2017 19:37:18 GMT 8
Speaking of calendars, here's an idea for a dozenal calendar:



Post by Buffoonery on Jan 14, 2017 19:48:43 GMT 8
Notes for the attachments above: This is not my idea, this comes from a man named Paul Rapoport. dozenal.aeweb.ca/pdf/calendarintro.pdfAlthough he used the 12 astrology signs which I personally don't like. Instead, I would like the months to be starting in the Spring now that I think of it. I'll make those changes now. Yeah, it makes a lot more sense to start in the spring.



Post by Buffoonery on Jan 14, 2017 20:02:11 GMT 8

