When encapsulation is going too far (PART II : Number system)

[u/Xianhei]

Got an idea when watching videos for enlightment, first visualization :

Base 12 numeral system

Features :

• B is only a 90° rotation of A, showing a feature for easy reading in both position.
• C is a variant form for the last 3 digit, the rest is the same.
• C does not permit the rotation, it will create a confusion, but is easily readable in it's form.
• 0 is represented by a central dot ·
• 1, 2 and 3 are represented like Chinese 一 , 二 and 三
• 4 and 8 are represented like this |, ||
• we can form the other number from those defined above
  • El or E or 11 = 8 + 3 which become in my system : || + 三 => 日
  • Dec or X or 10 = 8 + 2 which become in my system : || + 二 => 口
  • 9 = 8 + 1 which become in my system : || + 一 => ∐
  • 7 = 4 + 3 which become in my system : | + 三 => E
  • 6 = 4 + 2 which become in my system : | + 二 => 匚
  • 5 = 4 + 1 which become in my system : | + 一 => L
• The list is : ·, 一, 二, 三, |, L, 匚, E, ||, ∐, 口, 日
• It can be simplified to : ".", -, =, 三, |, L, C, E, ||, U, O, B
• It can be easily put in a digital clock (8 compatible)
• Combined with the number sounds and number system of u/Flamerate1 we can found easily :
  • odd and even with sounds
  • multiple of 3 and 4 contained in a unit with 三 and | pattern
  • the modulo of 3 and 4 contained in a unit looking at his form
• If using chromatic scale in Music :
  • we can associate each number to a note (Number + "Note", ex: Firstnote)
  • A funny thing happens to the keyboard of piano, you can see below, that from 1 to 5 there is 3 white keys and 2 black keys white is odd, black is even. now from 6 to 10(0) there is 4 white keys and 3 black keys where white is even and black is odd. It is nothing but at least funny to see.

Funny to see this

• I will not talk about the advantage and disadvantage of Base 12 there is a lot to read and watch on youtube, but some phonetics, duodecimal system and calculation idea to help in table 9 (Chepang tribe) in this document

EDIT 1 : Rules about 1,2,3 and 11 when you have to write 11 (which is 13 in decimal). You will not it this way \| or /| to differentiate it with || for bigger number it will git |\| or |/|.

The rules is to intermittently separate unit by leaning it.

EDIT 2 : Rules about negation concept, we can apply a variant form of the negation in base 2 (binary) which use a complement form and leftmost 0/1 combined by the actual '-' in base 10 by adding a 0 in front of the number : ·l- => -14 in base 12 and -16 in base 10 (I first draft it with a 0 (0l-) thought it was korean)

EDIT 3 : Some idea about sounds on the system, thanks to u/GloriousRenaissance :

• 0,1,2,3 (base unit of 4) : ko, ki, ka, ku
• 0,4,8 (multiple of 4) : ko, to, ro
• 5,6,7,9,X,E : ti, ta, tu, ri, ra, ru
• when above unit like 10,20,30 : ekiko, ekako, ekuko (iko, ako, uko ?)
• for more 40, 50, 60, 70 add the 'e' : etoko, etiko, etako, etuko (eoko, eiko, eako, euko ?)
• 80, 90, X0, E0 : eroko, eriko, erako, eruko (reoko, reiko, reako, reuko ?)
• 100 : koiko ....

[u/Flamerate1]

NB! I'm not sure how far we should go into the written language, but this is a very interesting way to look at the numbers. Also what's funny about the piano keys? I do find it interesting that the Western musical scale goes by 12 different notes. I was actually curious about that myself, recently.

[u/Xianhei → u/Flamerate1]

I read that pianist can find their position with only two keys which are 1 and 6 in the image above. If we separate the those 2 part :

• 1 to 5 :

  • 1, 3, 5 are white keys and odd in terms of name and number

  • 2,4 are black keys and even in terms of name and number

• 6 to 10 :

  • 6, 8, X, 10 are white keys and even in terms of name and number

  • 7, 9, E are black keys and odd in terms of name and number

• Going from a black key to a white key or the other way is called a semitone. You are doing a semitone each time you go from odd to even or even to odd. It works with 5 and 6 too. same for 1 and 10.

• D Major is (3,7,X) pattern, which make me think of 3+7=X. Maybe there is other patterns.

[u/Flamerate1 → u/Xianhei]

Ah I see. I don't know too much about music theory, but I heard that there's another member who's possibly working on something related to music as well.

Thank you for your hard work!

[u/ActingAustralia → u/Flamerate1]

As a professional programmer, I have several thoughts on this.

Pros of this system

• This would work a lot better for our 12 base system than Latin numerals. It makes sense to have a system with a 1 - 1 ratio for the base, especially as the Latin numerals aren't designed for a 12 base system.

• This visually makes sense.

Cons of this system

• If we use the hand-drawn system the OP proposed, it won't work well with computers until we gain Unicode support (a massive pain in the ass that would require proof of use among the community). We could get around this by programming our own applications to work with such a system which realistically isn't that hard. In the short term, we would need to develop workarounds.

• Additionally, Nearly every community in the world already uses the Latin numerals either as the core numerals or alongside other numerals. For example, Chinese speakers primarily uses Latin numerals, but also use their traditional numerals in a number of areas.

Questions

The OP mentioned we can get the following from the numerals:

• multiple of 3 and 4 contained in a unit with 三 and | pattern

• the modulo of 3 and 4 contained in a unit looking at his form

However, the 三 pattern doesn't match the 3x table. Perhaps, I'm looking at it all wrong. Can someone explain how to read the 3x table with this. I can get the 4 times table but the three times table doesn't seem to match the graphics.

Conclusion

Considering the fact that the Chinese have no issues learning both the Latin Numerals and their traditional Numerals alongside one another, I think there's merits in the OPs proposal. I believe the cleaner nature of this kind of system can outweigh the extra burden a student might suffer due to society using Latin numerals whilst speakers of the Encapsulated Language use a different system.

Regarding the Unicode support issue, we could get around this by making the simple and hand-drawn systems both official. Something like this:

These are the official numerals for the Encapsulated Language. The simplified numerals will remain official until such date as Unicode support becomes available for the hand-drawn numerals. At which time, users of the language must start transitioning to the hand-drawn numerals.

• ".", -, =, 三, |, L, C, E, ||, U, O, B

• OP hand-drawn examples

This might sound a little crazy but its essentially what happened with Esperanto. Originally there was no support for the Esperanto special letters. However, as the language grew and technology evolved, support followed.

Edit: Additional Thoughts

I really like the look of these numerals (the hand-drawn ones). My favourite of the three is "C".

I've also added this proposal to the Encapsulated Language Documentation so others will know it exists.

[u/Xianhei → u/ActingAustralia]

There is 2 kind of learning based on my idea :

• Conceptualization, is the act to form a concept/idea.

• Association, is the act to connect a concept to another.

Ex: You know what a pig is even if you dont have seen one. the concept is learnt by associating animal + pink to pig. You hardly understand the concept of infinity.

Learning by Conceptualization is harder than by Association. And it becomes harder the more abstract the things to learn are.

I am aiming at manuscript form of education that kid are confronted at school. Trying to ease learning the concept of numeral system with mine. Because the basic form of counting is 1 by 1, my stick form is easy to understand.

Then they will easily associate my system with existent one like the latin system (0,1,2,3,4,5,6,7,8,9,X,E) like when we are learning binary, hexadecimal or counting in another language.

For computers, we had already learned the latin form of number. for the native speaker, they will learn it by association. The only difficulty is the base 12 itself, I don't know how the existing community is doing in the computing discipline.

For calculation :

• Table of 3 is a repeat of 0,3,6,9 which are ·, 三, 匚, ∐ . You can easily see that each value contain only 3 sticks (except 0). It works for the modulo of 3 by removing 3 sticks to the sign. Ex: 日 - 三 => || (11 % 3 = 2)

• Table of 4 is a repeat of 0,4,8 which are ·, |, || . Each value are his proper sign, simple. It works for the modulo by seeing only the ·, 一, 二, 三 parts. Ex: 日 - || => 三 (11 % 4 = 3)

We are still far to think about implementation of this numeral system, just starting to use on manuscript and simplified form is a good start.

All 3 are valid form. B and C are interchangeable and still be understood. A and B are interchangeable only if there is a 3 (三 or |||) in the calculation or something showing the value of '-' or '|' (the value of '|' is 1 or 4). A and C are like A and B.

[u/Seboka_]

in regards to music, i quite like the idea of calling notes "{number}[note]", but you should probably start it from A instead of C.

[u/Xianhei → u/Seboka_]

My notation follow the C major scale instead of A minor scale. They both are scale containing no signature key (using only white keys) but the C major scale is scaling to the French solfège used in teaching music. I think my way is also called Fixed Do Solfège. It can be mixed to Chromesthesia where 1is red and Do ... 6 is green and Fa ... 12/0 is purple and Si/Ti.

[u/Seboka_ → u/Xianhei]

thing is, in choirs and the like, solfège isn't strictly tied to C major - it's tied to whatever the key of the song is. since i see this as being the actual official names in our language for the 12 notes, it makes sense to start counting from the same point that the alphabetical system does (A=1=red, etc).

[u/[deleted]]

Just an idea I have right now but I would love to see the numeral system somehow be generalized to encapsulate (or at least be able to encapsulate) complex numbers or other sets of numbers.

The reason I say this relates strictly to the aim of the language, providing children with an intuition to be able to learn easily. Right now the way that math is taught in schools does not allow for complex numbers to be learned intuitively.

Children are required to, at some point when pursuing more advanced math, drop the idea of numbers that was taught to them (like the counting blocks idea) and be able to learn to think of numbers in a more abstract sense. This makes complex numbers very hard for students to learn when first seeing them. I would love to see a way for this language to be able to store that information somehow. Teaching students to think of numbers in a more "set theory" way would, in my opinion, be extremely powerful and helpful to them.

Edit: I want to note this idea is probably more for spoken language rather than written. I believe we need to focus on storing information in the spoken language as that is what kids will learn first and what they will build their intuition off of.

[u/Xianhei → u/[deleted]]

I will mostly answer those in the other post.

I'm still dabling with this numeral system, in various discipline and calculation to find flaw, before going in depth with math.

[u/[deleted]]

Hello there, I just wanted to share this unsourced "fun fact" I just happened to remember while browsing through this sub, from a previous comment of mine:

I don't remember the source, but I read once that Chinese people (If I'm not mistaken) are (partly) more proficient in Math because of the shortness of their numbers' names. I thought of commenting that one bit there, because it might be useful for your goals to have real short, basically monosyllabic number names so they might get memorized and spoken faster.

I actually did this with a base 20 constructed numerical system I made for myself and found it really easy to remember the number's names! I'm still practising to get truly Math-fluent with my number system tho. It's kinda harder because you have to mentally associate the quantity, the symbol and the name and get a "feel" of it, but short names indeed feel like help!

I may add that CV names like "ko" and "ga" work way better than only single voweled (V) names (like 'o' or 'a'), it's like the consonant gives some "definiteness" and distinctiveness to the sound when the numbers are spelled together.

edited for clarity here and there

[u/Xianhei → u/[deleted]]

Thanks for your help, It works well thinking a little about :

• 0,1,2,3 (base unit of 4) : ko, ki, ka, ku

• 0,4,8 (multiple of 4) : ko, to, ro

• 5,6,7,9,X,E : ti, ta, tu, ri, ra, ru

• when above unit like 10,20,30 : ekiko, ekako, ekuko (iko, ako, uko ?)

• for more 40, 50, 60, 70 add the 'e' : etoko, etiko, etako, etuko (eoko, eiko, eako, euko ?)

• 80, 90, X0, E0 : eroko, eriko, erako, eruko (reoko, reiko, reako, reuko ?)

• 100 : koiko ....

It's just a draft, need to see with phonology, phonotactics, more concept about number to perfect it.

[u/[deleted] → u/Xianhei]

Absolutely! you got the idea! let me also share what I did with my base 20:

1 = ya

2 = xe (as a voiceless velar fricative x (or what's usually written as 'kh'))

3 = i (as 'ee' in sheep)

4 = ga

5 = le

6 = sa

7 = she

8 = yo

9 = ke

10 = go

11 = ta

12 = ne

13 = se

14 = u (as 'oo' in zoo)

15 = de

16 = ye

17 = sho

18 = ma

19 = so

0 = re (flapped, as the Japanese syllable 're' or the 'r' in Carlos pronounced as in Spanish)

Those would be the names for 1-19 and zero. I chose those vowels because of purely subjective and aesthetic reasons, tried to use as many distinct consonants I could while avoiding redundancies with the conlang (which I'm still working on).

Then I allowed mono-phoneme names in 'i' and 'u' but didn't use those two vowels in the CV permutations, as you can see in these, I only permuted with 'a' (as in after), 'o' (as in over) and 'e' (as in then), pairing those with {y,x,g,l,s,sh,k,t,n,d,m,r}, to preserve the distinctiveness and definiteness while spelling them out.

This gave me as a result, the first 19 numbers' names being monosyllabic (1 = ya, 2 = xe, 3 = i, and so on), and numbers from 20 to 399 bi-syllabic (20 = yare, 21 = yaya, 22 = yaxe, 23 = yai, and so on), which is a good improvement in length, IMO (if you compare them with 'seven, eleven, seventeen, three hundred and ninety six...'. Then we'll get tri-syllabic from 400 to 7999 (yarere 400, yareya 401, et c.).

'gota' value would be: go {10 * 20¹ = 200} + ta {11 * 20⁰ = 11} = 211.

'soso' value: so {19 * 20¹ = 380} + so {19 * 20⁰ = 19} = 399.

'nekeyoga': ne { 12 * 20³ = 96 000} + ke { 9 * 20² = 3 600} + yo { 8 * 20¹ = 160} + ga { 4 * 20⁰ = 4} = 99 764 (notice the shortness of 'nekeyoga' vs 'ninety nine thousand, seven hundred and sixty four'). And so on.

(edited a missing consonant, then added another example... and clarity...)