Continued from here. All credit goes to /u/a-username-for-me and /u/fourteensquares, but the latter got locked out of reddit at the last minute
The next get is at 43 0000.
Base six is the REAL best base/numeral system. All of the values below 10 (ie, six) are either:
- A factor of 10, or a multiple of a factor of 10
- a unit whose multiples count either forward or backward when expressed in mod_10 (that is, either 1 or 5):
| 1*1 = 1mod10 | 1*2 = 2mod10 | 1*3 = 3mod10 | . . . etc. |
|---|---|---|---|
| 5*1 = -1mod10 | 5*2 = -2mod10 | 5*3 = -3mod10 | . . . etc. |
Everyone easily memorizes how to multiply by nine in our janky base-ten number system thanks to this second property: 9, 18, 27, 36 . . . the digits always nicely add up to nine.
In base six, five has this property instead:
| 5*1 = 5 | 5*2 = 14 | 5*3 = 23 | 5*4 = 32 | 5*5 = 41 | 5*10 = 50 |
|---|
(Our whole multiplication table looks like this):
| XY =* | 1 | 2 | 3 | 4 | 5 | 10 |
|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 10 |
| 2 | 2 | 4 | 10 | 12 | 14 | 20 |
| 3 | 3 | 10 | 13 | 20 | 23 | 30 |
| 4 | 4 | 12 | 20 | 24 | 32 | 40 |
| 5 | 5 | 14 | 23 | 32 | 41 | 50 |
| 10 | 10 | 20 | 30 | 40 | 50 | 100 |
As for decimal representations, recall how ugly one seventh is in base ten:
0.>!142857!< . . . (repeating)
There is actually a nice pattern here, but this is still ridiculous. Why should we need six digits to represent this small-number division problem? We shouldn't. The only reason we do:
Seven is neither a factor of ten, nor a multiple of a factor of ten, nor one-mod-ten, nor negative-one-mod-ten, and using ten as a base was an objectively terrible decision.
Lets see how base six fixes things (using the spoiler tag to indicate the repeating portion - spot the patterns as you go down the columns).
| 1/1 = 1 | 1/2 = 0.3 | 1/3 = 0.2 | 1/4 = 0.13 | 1/5 = 0.>!1!< | 1/10 = 0.1 | 1/11 = 0.>!05!< | 1/12 = 0.043 | 1/13 = 0.04 | 1/14 = 0.0>!3!< |
|---|---|---|---|---|---|---|---|---|---|
| 2/1 = 2 | 2/2 = 1 | 2/3 = 0.4 | 2/4 = 0.3 | 2/5 = 0.>!2!< | 2/10 = 0.2 | 2/11 = 0.>!14!< | 2/12 = 0.13 | 2/13 = 0.12 | 2/14 = 0.>!1!< |
| 3/1 = 3 | 3/2 = 1.3 | 3/3 = 1 | 3/4 = 0.43 | 3/5 = 0.>!3!< | 3/10 = 0.3 | 3/11 = 0.>!23!< | 3/12 = 0.213 | 3/13 = 0.2 | 3/14 = 0.1>!4!< |
| 4/1 = 4 | 4/2 = 2 | 4/3 = 1.2 | 4/4 = 1 | 4/5 = 0.>!4!< | 4/10 = 0.4 | 4/11 = 0.>!32!< | 4/12 = 0.3 | 4/13 = 0.24 | 4/14 = 0.>!2!< |
| 5/1 = 5 | 5/2 = 2.3 | 5/3 = 1.4 | 5/4 = 1.13 | 5/5 = 1 = 0.>!5!< | 5/10 = 0.5 | 5/11 = 0.>!41!< | 5/12 = 0.343 | 5/13 = 0.32 | 5/14 = 0.3 |
| 10/1 = 10 | 10/2 = 3 | 10/3 = 2 | 10/4 = 1.3 | 10/5 = 1.>!1!< | 10/10 = 1 | 10/11 = 0.>!50!< | 10/12 = 0.43 | 10/13 = 0.4 | 10/14 = 0.>!3!< |
| 11/1 = 11 | 11/2 = 3.3 | 11/3 = 2.2 | 11/4 = 1.43 | 11/5 = 1.>!2!< | 11/ |
This is senary, 0-5.
Thanks to /u/basskro and /u/TehVulpez for the final run and the assist and to all the counters in this thread.
The next get is 32 0000.
Continued from here. Big ups to /u/kongburrito for the counts!
With this get, 10 of the top 20 longest running side threads are base threads. Heh.
The next get is at 24 0000.
I'm not super experienced in math, but I do love it.
I know stuff like using Dozenal is kind of a cliche math topic, the kind people can tend to roll their eyes at, but I'm just having fun thinking about it so I don't really care. I think it'd be cool, say, if I'm figuring something out in probabilities I can switch to Senary because I'm using d6's. Or something.
Right now I'm interested in Senary. Or Seximal. Or Heximal, as it should be but the name is taken.
Putting aside whether anyone would actually use it, or whether it's the 'best' system. I just think they're a super cool way to change your perspective.
I haven't found a lot about making it more immediately useful or digestible, though. What I mean by that: If not to reduce the required mental gymnastics to convert from base 10, then to improve the mental gymnastics so it's a little easier. If that makes sense? I'm looking for little tricks basically.
One reason I like senary is while 5 isn't a factor, it's still adjacent so it makes it easier to manage fifths.
What I'm wondering is if you can leverage the fact that 5 is to 6 as 9 is to 10, to make converting between them easier to do?
So for a simple example: What if you thought of base 6 as base 5+1? Would that complicate or simplify things? I'm thinking this because I'm base 10 native, grouping things in 5's comes very naturally. But wrapping my head around the pacing of 6 exponents I'm finding is very difficult.
Amateur question, I'm sure, so I hope you'll be patient with me.
I'm thinking in application it would be cool to like convert a d6 based game into senary, and play it that way as a way to practice or just geek out about it? Like a tabletop RPG or something. I dunno. You could even use dice as a visual numerical display, and that just gets me going.
Thoughts?
Continued from here.
Thank you to /u/Chalupa_Dad for the run and assist!
This is counting in base 6, meaning you only use digits 0-5. The next get will be at 15 0000; good luck, and happy counting!
Continued from here.
Thank you to /u/piyushsharma301 for the closing run and assist, and /u/orangey10 for the earlier run!
IMPORTANT NOTICE: Upon discussion between a mod and the original creator of the senary counting, the decision has been made that a get will occur at every additional 1 0000 (1,296 counts), rather than at the original mark of 5000 (1,080 counts). Thus, the next get will be at 10 0000.
counting in base 6.
glad to see me, the creator of senary, achieve a get, after about a year after the commencement of the thread. thanks to u/smarvin6689 for helping me out with the late run and the assist, and also being the most prominent counter in all of senary, beating me by over twice my counts. thanks to all the counters for helping my thread to now reach 11,664 in decimal. maybe we'll make top 20 side threads next!
continued from here
https://www.reddit.com/r/counting/comments/m9bafo/senary_40_0000/gxm8mdx/?context=3
next get is 42 0000
continued from here
the next get is at 40 0000
Continued from here
Thanks to nonsensy for the final run and congrats on the assist. And thanks for pinging me so I remembered the thread
The next get is 40 0000
Continued from here. Congrats to /u/PaleRulerGoingAlone7 for the get! I'll make this thread in his place, as he had to go to a meeting.
The next get is at 35 0000.
Continued from here. Thanks to /u/nonsensy for the run and to all others for the thread counts!
> This is senary, 0-5.
The next get is at 33 0000.
Continued from here.
Thanks to a-username-for-me for the finish, and everyone else for the counts.
The next get is at 30 0000.
Continued from [here] (https://www.reddit.com/r/counting/comments/9fxt47/senary_21_0000/edridlo/)
Thanks /u/TheNitromeFan for the last few counts.
Next get is 23 0000.
Continued from here
Thanks to u/TheNitromeFan for the counts. I'm sure he has some more fun stats about this side thread than I do.
The next get should be 25 0000
1/2 = 0.3
1/3 = 0.2
1/4 = 0.13
1/5 = 0.(1)
1/10 = 0.1
1/11 = 0.(05)
1/12 = 0.043
1/13 = 0.04
1/14 = 0.0(3)
1/15 = 0.(0313452421)
1/20 = 0.03
1/21 = 0.(024340531215)
1/22 = 0.0(23)
1/23 = 0.0(2)
1/24 = 0.0213
1/25 = 0.(0204122453514331)
1/30 = 0.02
1/31 = 0.(015211325)
1/32 = 0.01(4)
1/33 = 0.0(14)
1/34 = 0.0(1345242103)
1/35 = 0.(01322030441)
1/40 = 0.013
1/41 = 0.(01235)
1/42 = 0.0(121502434053)
1/43 = 0.012
1/44 = 0.01(14)
1/45 = 0.(01124045443151)
1/50 = 0.0(1)
1/51 = 0.(010545)
1/52 = 0.01043
1/53 = 0.0(1031345242)
1/54 = 0.0(1020412245351433)
1/55 = 0.(01)
1/100 = 0.01
Counting in base 6; continued from here.
Thank you to /u/Urbul for the run and assist!
Next get is at 1 4000.
Ouiqueasse convention is using already existing positive digits for negative numbers (like 7 being -3 in Ouiqueasse-Convention Base 10)
Numbers would be -2 - 5
-1 - 4
0 - 0
1 - 1
2 - 2
3 - 3
4 - 15
5 - 14
6 - 10 And further on.
Start at 1, get is at 155355 (I think 4344 in standard Senary, which is 1000 in DecinL
Continued from here. Major props to /u/Chalupa_Dad for the 360+ count run and assist!
The next get is at 21 0000.
Continued from here.
The get is at 4 1000.
Continued from here.
Thank you to /u/qwertylool for the closing run and assist!
Next get is at 3 2000.
Senary= Base 6. get is 5000, i think that's 1080??
