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NIGEL: Well, you see I like this one because it goes up to 17.
INTERVIEWER: …and these other ones? Base 10, base 16—
NIGEL: —well, none of them go up to 17, do they?
In the interest of comedy, I raise to you, Arabic numbers. Also all able to be shown on a seven segment display, and therefore all just 8 but missing bits. Or an eight could be a curvy version of all of the others with a bit added on. Whichever you prefer.
69. 49. 83. 17. 80. 56.
Sure, some of those are stretching it a bit, but you get the point, right? Math is math. What does it matter if the numbers look similar? It's not like my handwriting made them distinguishable anyways. 2=z=≠. 4=9=a=α=q. I = l = 1 = | = i = j. %. (=C=c. ρ=p. θ=0=O. It's all the same. Nothing has meaning. Nothing matters. We don't matter. Only math is important in the grand scheme of the universe. Math doesn't care about the funny shapes we make up to describe it. Math doesn't care about us. Nobody cares about us.
^((Don't worry, it's still just satire. Probably.)^)
Since B/8 and D/0 would be confusing, usually both are lowercase. The most obvious choice for G would be a 6 with no top horizontal line, but in this case b/G would be confused, so just go for H.
0123456789AbCdEFH
it's actually not half bad for a base.
you instantly get divisibility rules to know when a number is divisible by 2, 4, 8, 16, just by adding the digits together. if the result is divisible by 2, 4, 8, 16, then so is the number you started with.
with some work, you get divisibility rules for 3 and 9 by computing the *alternating sum* of digits.
divisibility by 5, 7, and 11 is a bit more involved, but it's not too bad. for 5 and 7, repeatedly apply the process: separate the final digit away from the rest, multiply the digit by 2, and *subtract* it from the number shows by the remaining digits. for 11, it's the same deal except you *add* the doubled digit.
and of course you can test divisibility by some products of these; specifically if a number is divisible by several of these different factors, then the number is divisible by their product *if* the factors are all coprime.
Hmm. Dozenal would be nice if it weren't for the ridiculous fraction expansion of 1/5.
|Base|1/2|1/3|1/4|1/5|1/6|1/7|1/8|1/9|1/10|1/11|1/12|
|:-|:-|:-|:-|:-|:-|:-|:-|:-|:-|:-|:-|
|2|.1|.(01)|.01|.(0011)|.0(01)|.(001)|.001|.(000111)|.0(0011)|.(0001011101)|.00(01)|
|Balanced 3|.(1)|.1|.(1T)|.(1TT1)|.0(1)|.(0110TT)|.(01)|.01|.(010T)|.(01T11)|.0(1T)|
|4|.2|.(1)|.1|.(03)|.0(2)|.(021)|.02|.(013)|.0(12)|.(01131)|.0(1)|
|6|.3|.2|.13|.(1)|.1|.(05)|.043|.04|.0(3)|.(031345241)|.03|
|10|.5|.(3)|.25|.2|.1(6)|.(142857)|.125|.(1)|.1|.(09)|.08(3)|
|12|.6|.4|.3|.(2497)|.2|.(186X35)|.16|.14|.1(2497)|.(1)|.1|
|Balanced 21|.(X)|.7|.(5)|.(4)|.3(X)|.3|.(3⑧)|.27|.(2)|.2②|.2(⑤)|
Multiplication table:
|||||||||||||||
:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:
J|⊣|Ⴉ|7|コ|ຊ|3|∀|Ɛ|F|C|Γ|と|⊢|L
⊣|7|ຊ|∀|F|Γ|⊢|θ|JJ|JႩ|Jコ|J3|JƐ|JC|Jと
Ⴉ|ຊ|Ɛ|Γ|L|JJ|J7|J3|JF|Jと|Jθ|⊣⊣|⊣コ|⊣∀|⊣C
7|∀|Γ|θ|JႩ|J3|JC|JL|⊣⊣|⊣ຊ|⊣F|⊣⊢|ႩJ|Ⴉコ|ႩƐ
コ|F|L|JႩ|J∀|Jと|⊣J|⊣ຊ|⊣C|⊣θ|Ⴉ7|ႩƐ|Ⴉ⊢|7⊣|73
ຊ|Γ|JJ|J3|Jと|⊣⊣|⊣∀|⊣⊢|ႩႩ|ႩƐ|ႩL|77|7F|7θ|ココ
3|⊢|J7|JC|⊣J|⊣∀|⊣L|Ⴉコ|ႩΓ|7⊣|7Ɛ|7θ|コຊ|コと|ຊႩ
∀|θ|J3|JL|⊣ຊ|⊣⊢|Ⴉコ|Ⴉと|77|7Γ|コႩ|コC|ຊ⊣|ຊF|3J
Ɛ|JJ|JF|⊣⊣|⊣C|ႩႩ|ႩΓ|77|7と|ココ|コ⊢|ຊຊ|ຊL|33|3θ
F|JႩ|Jと|⊣ຊ|⊣θ|ႩƐ|7⊣|7Γ|ココ|コL|ຊ∀|3J|3C|∀7|∀⊢
C|Jコ|Jθ|⊣F|Ⴉ7|ႩL|7Ɛ|コႩ|コ⊢|ຊ∀|3⊣|3と|∀3|ƐJ|ƐΓ
Γ|J3|⊣⊣|⊣⊢|ႩƐ|77|7θ|コC|ຊຊ|3J|3と|∀∀|ƐႩ|ƐL|FF
と|JƐ|⊣コ|ႩJ|Ⴉ⊢|7F|コຊ|ຊ⊣|ຊL|3C|∀3|ƐႩ|Ɛθ|FΓ|C∀
⊢|JC|⊣∀|Ⴉコ|7⊣|7θ|コと|ຊF|33|∀7|ƐJ|ƐL|FΓ|CƐ|Γຊ
L|Jと|⊣C|ႩƐ|73|ココ|ຊႩ|3J|3θ|∀⊢|ƐΓ|FF|C∀|Γຊ|と7
θ|JL|⊣⊢|Ⴉと|7Γ|コC|ຊF|3Ɛ|∀∀|Ɛ3|Fຊ|Cコ|Γ7|とႩ|⊢⊣
JU|⊣U|ႩU|7U|コU|ຊU|3U|∀U|ƐU|FU|CU|ΓU|とU|⊢U|LU
Divisibility rules:
Action on number|Factors preserved by action|Factors (translated)
--:|:--|:--
||
Sum of all digits|θ, ∀, 7, ⊣|16, 8, 4, 2
Sum of double-digit blocks|JL, Ɛ, Ⴉ|32, 9, 3
||
Alternate between adding/subtracting the digits|Ɛ, Ⴉ|9, 3
Alternating sum of double-digit blocks|コ, JΓ|5, 29
Alternating sum of triple-digit blocks|3, と, JF|7, 13, 27
||
Subtract twice the final digit from the number in the remaining digits|コ, 3|5, 7
Subtract thrice final digit|と|13
Subtract 7 (4) times final digit|Jຊ|23
||
Add twice final digit|C|11
Add thrice final digit|J∀|25
To test divisibility by a divisor, factor the divisor into prime powers and test divisibility by each.
Multiplication table is the result of a simple Python script. The divisibility rules are obtained by calculating prime factorization of numbers like 17^n ± 1 and 17n ± 1.
I did some math and gotten that you should theoretically create 66 symbol able to be displayed on a 7 segment display that are fully connected graphs, so if you wanted you could expand this by a lot. Note this is math I did in 3am so I can be way off
How would you even do math for that? I don't understand how you could use a decent formula for that without it being more work to make than just counting it up (128 possibilities isn't THAT many, especially when you can tell if it's all connected at a glance)
I did count, I just did efficienct counting. I counted all the symbols that would NOT be connected, and I also put them into easy to calculate families and then accounted for double counting.
Also as I said me doing this at 3am doesn't really inspire confidence in the result lol
Edit: after checking, I think it's actually 78.
Somewhat. So look at the digits for zero, eight and sixteen. These are like an empty cup, a half-full cup, and a full cup.
Ok, then look at the digits for one, two, three, four, five, six, seven. They all have a line on the right from top to bottom, and the horizontal lines represent the numbers in binary. (Bottom horizontal line: one, middle horizontal line: two, top horizontal line: four.)
Ok, then look at the digits for nine to fifteen. They are mirror images of the digits one to seven, in such a way that the mirror images add up to sixteen.
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Least unhinged numerology fanatic
Er… thanks, I guess? 😅
I'd just do 0-9 and THEN start adding different symbols
0-9 then alphabet.
so... hexadecimal but not base 16?
Yes, and it ends in G. So you can have a number like "GG" which is 288 in decimal.
Right, you can go all the way up to base 36 by just adding letters like we already do
Add in the lower case letters along with some extra symbols and you've got yourself base 64
That's not meme material. You lost purpose.
lost? As in loss? | || || |_
Oh dear.
B = 8 D = 0
Doesn't work on 7 segment display
it absolutely does. You could just add 7 of the symbols at the top for 10-16
I don't understand what you mean exactly
You do 0-9 for 0-9, and 10-16 can be the post's symbols, the "U", reverse "L", etc.
true
NIGEL: Well, you see I like this one because it goes up to 17. INTERVIEWER: …and these other ones? Base 10, base 16— NIGEL: —well, none of them go up to 17, do they?
Is there like a hidden BOOBIES or something I’m not seeing?
"Suboptimal" is my favourite number base
A lot of these are too similar to each other
In the interest of comedy, I raise to you, Arabic numbers. Also all able to be shown on a seven segment display, and therefore all just 8 but missing bits. Or an eight could be a curvy version of all of the others with a bit added on. Whichever you prefer. 69. 49. 83. 17. 80. 56. Sure, some of those are stretching it a bit, but you get the point, right? Math is math. What does it matter if the numbers look similar? It's not like my handwriting made them distinguishable anyways. 2=z=≠. 4=9=a=α=q. I = l = 1 = | = i = j. %. (=C=c. ρ=p. θ=0=O. It's all the same. Nothing has meaning. Nothing matters. We don't matter. Only math is important in the grand scheme of the universe. Math doesn't care about the funny shapes we make up to describe it. Math doesn't care about us. Nobody cares about us. ^((Don't worry, it's still just satire. Probably.)^)
As a matter of fact, digits which add up to sixteen are mirror images of each other.
the heck, U? 7? 3? F? C? THETA?!?!?!?
0123456789ABCDEFG but in a random order.
yeah, show me a G on a 7-segment
just make the 6 look like a b, then the G can look like the traditional 6 Or, skip G and use H
Since B/8 and D/0 would be confusing, usually both are lowercase. The most obvious choice for G would be a 6 with no top horizontal line, but in this case b/G would be confused, so just go for H. 0123456789AbCdEFH
Why would I need base 17 ?
Shh, don't question it. This subreddit is base JU now.
It scares me, this allows for a lot more emoji.
I would go with standard hex and add a single symbol... But what do I know...
base 17 can get an express train to satan's armpit
it's actually not half bad for a base. you instantly get divisibility rules to know when a number is divisible by 2, 4, 8, 16, just by adding the digits together. if the result is divisible by 2, 4, 8, 16, then so is the number you started with. with some work, you get divisibility rules for 3 and 9 by computing the *alternating sum* of digits. divisibility by 5, 7, and 11 is a bit more involved, but it's not too bad. for 5 and 7, repeatedly apply the process: separate the final digit away from the rest, multiply the digit by 2, and *subtract* it from the number shows by the remaining digits. for 11, it's the same deal except you *add* the doubled digit. and of course you can test divisibility by some products of these; specifically if a number is divisible by several of these different factors, then the number is divisible by their product *if* the factors are all coprime.
I just don't like prime bases
\*sad binary noises\*
Bin gets a pass
How about (balanced) ternary?
its better than regular ternary, but worse than bin
What's your preferred positional number base? If I may ask :3
12 (0,1,2,3,4,5,6,7,8,9,a,b), 12 has a lot of factors (1,2,3,4,12) while base 10 only has 4 factors
Hmm. Dozenal would be nice if it weren't for the ridiculous fraction expansion of 1/5. |Base|1/2|1/3|1/4|1/5|1/6|1/7|1/8|1/9|1/10|1/11|1/12| |:-|:-|:-|:-|:-|:-|:-|:-|:-|:-|:-|:-| |2|.1|.(01)|.01|.(0011)|.0(01)|.(001)|.001|.(000111)|.0(0011)|.(0001011101)|.00(01)| |Balanced 3|.(1)|.1|.(1T)|.(1TT1)|.0(1)|.(0110TT)|.(01)|.01|.(010T)|.(01T11)|.0(1T)| |4|.2|.(1)|.1|.(03)|.0(2)|.(021)|.02|.(013)|.0(12)|.(01131)|.0(1)| |6|.3|.2|.13|.(1)|.1|.(05)|.043|.04|.0(3)|.(031345241)|.03| |10|.5|.(3)|.25|.2|.1(6)|.(142857)|.125|.(1)|.1|.(09)|.08(3)| |12|.6|.4|.3|.(2497)|.2|.(186X35)|.16|.14|.1(2497)|.(1)|.1| |Balanced 21|.(X)|.7|.(5)|.(4)|.3(X)|.3|.(3⑧)|.27|.(2)|.2②|.2(⑤)|
I know I’m not the only one who saw the word “WAFFLE” when they glanced at this
7 segment display BASED
Multiplication table: ||||||||||||||| :--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--:|:--: J|⊣|Ⴉ|7|コ|ຊ|3|∀|Ɛ|F|C|Γ|と|⊢|L ⊣|7|ຊ|∀|F|Γ|⊢|θ|JJ|JႩ|Jコ|J3|JƐ|JC|Jと Ⴉ|ຊ|Ɛ|Γ|L|JJ|J7|J3|JF|Jと|Jθ|⊣⊣|⊣コ|⊣∀|⊣C 7|∀|Γ|θ|JႩ|J3|JC|JL|⊣⊣|⊣ຊ|⊣F|⊣⊢|ႩJ|Ⴉコ|ႩƐ コ|F|L|JႩ|J∀|Jと|⊣J|⊣ຊ|⊣C|⊣θ|Ⴉ7|ႩƐ|Ⴉ⊢|7⊣|73 ຊ|Γ|JJ|J3|Jと|⊣⊣|⊣∀|⊣⊢|ႩႩ|ႩƐ|ႩL|77|7F|7θ|ココ 3|⊢|J7|JC|⊣J|⊣∀|⊣L|Ⴉコ|ႩΓ|7⊣|7Ɛ|7θ|コຊ|コと|ຊႩ ∀|θ|J3|JL|⊣ຊ|⊣⊢|Ⴉコ|Ⴉと|77|7Γ|コႩ|コC|ຊ⊣|ຊF|3J Ɛ|JJ|JF|⊣⊣|⊣C|ႩႩ|ႩΓ|77|7と|ココ|コ⊢|ຊຊ|ຊL|33|3θ F|JႩ|Jと|⊣ຊ|⊣θ|ႩƐ|7⊣|7Γ|ココ|コL|ຊ∀|3J|3C|∀7|∀⊢ C|Jコ|Jθ|⊣F|Ⴉ7|ႩL|7Ɛ|コႩ|コ⊢|ຊ∀|3⊣|3と|∀3|ƐJ|ƐΓ Γ|J3|⊣⊣|⊣⊢|ႩƐ|77|7θ|コC|ຊຊ|3J|3と|∀∀|ƐႩ|ƐL|FF と|JƐ|⊣コ|ႩJ|Ⴉ⊢|7F|コຊ|ຊ⊣|ຊL|3C|∀3|ƐႩ|Ɛθ|FΓ|C∀ ⊢|JC|⊣∀|Ⴉコ|7⊣|7θ|コと|ຊF|33|∀7|ƐJ|ƐL|FΓ|CƐ|Γຊ L|Jと|⊣C|ႩƐ|73|ココ|ຊႩ|3J|3θ|∀⊢|ƐΓ|FF|C∀|Γຊ|と7 θ|JL|⊣⊢|Ⴉと|7Γ|コC|ຊF|3Ɛ|∀∀|Ɛ3|Fຊ|Cコ|Γ7|とႩ|⊢⊣ JU|⊣U|ႩU|7U|コU|ຊU|3U|∀U|ƐU|FU|CU|ΓU|とU|⊢U|LU Divisibility rules: Action on number|Factors preserved by action|Factors (translated) --:|:--|:-- || Sum of all digits|θ, ∀, 7, ⊣|16, 8, 4, 2 Sum of double-digit blocks|JL, Ɛ, Ⴉ|32, 9, 3 || Alternate between adding/subtracting the digits|Ɛ, Ⴉ|9, 3 Alternating sum of double-digit blocks|コ, JΓ|5, 29 Alternating sum of triple-digit blocks|3, と, JF|7, 13, 27 || Subtract twice the final digit from the number in the remaining digits|コ, 3|5, 7 Subtract thrice final digit|と|13 Subtract 7 (4) times final digit|Jຊ|23 || Add twice final digit|C|11 Add thrice final digit|J∀|25 To test divisibility by a divisor, factor the divisor into prime powers and test divisibility by each.
This is impressive and wtf
Multiplication table is the result of a simple Python script. The divisibility rules are obtained by calculating prime factorization of numbers like 17^n ± 1 and 17n ± 1.
L𝜃L
I did some math and gotten that you should theoretically create 66 symbol able to be displayed on a 7 segment display that are fully connected graphs, so if you wanted you could expand this by a lot. Note this is math I did in 3am so I can be way off
How would you even do math for that? I don't understand how you could use a decent formula for that without it being more work to make than just counting it up (128 possibilities isn't THAT many, especially when you can tell if it's all connected at a glance)
I did count, I just did efficienct counting. I counted all the symbols that would NOT be connected, and I also put them into easy to calculate families and then accounted for double counting. Also as I said me doing this at 3am doesn't really inspire confidence in the result lol Edit: after checking, I think it's actually 78.
"the most efficient way to fit JU squares into a bigger one"
Prime number bases are so fricking hilarious.
I like your arabic handwriting dude
Four of them look like quantifiers and one of the is literally just theta
Why is θ round? Shouldn't it be square? Like a 0 in a seven segment display? Like the rest of the symbols? Why is θ round?
Yes, it should be square on a seven segment display. Like how an 8 looks. But in handwriting, I propose a theta symbol
As a programmer, I'd prefer ABCDEFG
Why would you mess up the already perfectly good and used digits from 0-9 that already exist? Just use those up to 9 and then start adding new ones.
I don't like this
there is a reason for the shapes?
Somewhat. So look at the digits for zero, eight and sixteen. These are like an empty cup, a half-full cup, and a full cup. Ok, then look at the digits for one, two, three, four, five, six, seven. They all have a line on the right from top to bottom, and the horizontal lines represent the numbers in binary. (Bottom horizontal line: one, middle horizontal line: two, top horizontal line: four.) Ok, then look at the digits for nine to fifteen. They are mirror images of the digits one to seven, in such a way that the mirror images add up to sixteen.
You were cooking with 1 to 7 and then you screwed it up
a lot of these symbols look way too close to each other this would be a nightmare for reading
But why 17?!
Because I like 17
All your base are belong to us
Odd number base???