Why are Japanese characters not used in equations?


Why do Japanese texts/[scientific
articles](http://www2.yukawa.kyoto-u.ac.jp/~tetsuji.kimura/NOTEs/SCA_UU2.pdf)
not use kana/kanji in their equations? For example

[code]

    f(x) = x + 1
    
[/code]

instead of

[code]

    f(あ) = あ + 1
    
[/code]

I don't see the Cyrillic alphabet in equations either. Did someone once decide
to only use latin letters or has this just happened and people are used to
this convention?

* * *

Example: Japanese Wikipedia entry for "function" [![enter image description
here](https://i.stack.imgur.com/VMBGJ.png)](https://i.stack.imgur.com/VMBGJ.png)




Here are some facts, and my speculations.

## Actual Usuages

### Japanese as Text

In non-technical context, we can use arbitrary text (just like in English) in
equations:

> 長方形について， "面積 = 縦 × 横"

is a natural way of expressing the idea (so is "area = length × width").

Elaborating on this,

> 仕事 = ∫ 力・d(位置)

is very rarely seen but would be acceptable by most readers.

### Japanese character as a symbol

Interestingly, I found a rare case where a Japanese character is used in the
way you are looking for. On [_“The stack of higher internal categories and
stacks of iterated spans”_](https://arxiv.org/abs/1506.08870), page 13, they
have this notation: "The Yoneda embedding よ : C → P(C)" (No `\mathcal` shown
here)

[![「よ」 used for Yoneda
embedding](https://i.stack.imgur.com/fX5wS.png)](https://i.stack.imgur.com/fX5wS.png)

The author seems to have decided that 「よ」 for 「米田」 is a good choice.

### Other Alphabets

Latin and Greek alphabets are used everywhere. ℵ from Hebrew is a conventional
notation in set theory, and ב is used in [similar
contexts](https://en.wikipedia.org/wiki/Beth_number). I believe what alphabets
appear in equations mainly depends on conventions, rather than certain rules.

## Why Not?

This is only my speculations on why Japanese characters aren't popular in
equations.

  * Conventions, across the world. 
    * `f` for function. `x` for unknown. `F` for force, `e` for Euler, etc. `g` , being the successor of `f`, for another function. Certain conventions above are universal, and we don't really want to use different notations for discussions in Japanese and English. When you see x = a(f), you'll get slightly confused.
  * No one can read it 
    * There's no such thing as mathematics only for certain language community.
  * Latin alphabets are more suitable for notating with a single letter. 
    * 「か」 for 函数 really isn't appealing for me because it loses so much information. `函（変）= 正弦(変) + 2` looks interesting, but we can't have two variables (Kanji don't have natural succ/pred). 函(変1, 変2) = 変1× 変22 might be worth discussion. There's no practical benefits, though.
  * I have never been told _not_ to Japanese characters specifically. We just learn from what are widely used and stick with them, because that's the easiest for communication.

So I believe the answer is

  * It's just because it isn't conventional to do so, and there aren't many reasons to do so, actually.
  * If certain conventions are established (I'm hoping 「よ」 for 米田 to be among the first), that character for that usage will be seen everywhere.

* * *

  * [Related question in Math.stackexchange](https://math.stackexchange.com/q/165368).
  * My finding on the 「よ」 is attributed to the following tweet:

数学記号として平仮名が使われる時代が既に訪れていたのか...
[pic.twitter.com/1MENyIDSwC](https://t.co/1MENyIDSwC)

-- ウニ (@unununum_1) [4 May
2017](https://twitter.com/unununum_1/status/860125300104937472?ref_src=twsrc%5Etfw)




Here are some facts, and my speculations.

## Actual Usuages

### Japanese as Text

In non-technical context, we can use arbitrary text (just like in English) in
equations:

> 長方形について， "面積 = 縦 × 横"

is a natural way of expressing the idea (so is "area = length × width").

Elaborating on this,

> 仕事 = ∫ 力・d(位置)

is very rarely seen but would be acceptable by most readers.

### Japanese character as a symbol

Interestingly, I found a rare case where a Japanese character is used in the
way you are looking for. On [_“The stack of higher internal categories and
stacks of iterated spans”_](https://arxiv.org/abs/1506.08870), page 13, they
have this notation: "The Yoneda embedding よ : C → P(C)" (No `\mathcal` shown
here)

[![「よ」 used for Yoneda
embedding](https://i.stack.imgur.com/fX5wS.png)](https://i.stack.imgur.com/fX5wS.png)

The author seems to have decided that 「よ」 for 「米田」 is a good choice.

### Other Alphabets

Latin and Greek alphabets are used everywhere. ℵ from Hebrew is a conventional
notation in set theory, and ב is used in [similar
contexts](https://en.wikipedia.org/wiki/Beth_number). I believe what alphabets
appear in equations mainly depends on conventions, rather than certain rules.

## Why Not?

This is only my speculations on why Japanese characters aren't popular in
equations.

  * Conventions, across the world. 
    * `f` for function. `x` for unknown. `F` for force, `e` for Euler, etc. `g` , being the successor of `f`, for another function. Certain conventions above are universal, and we don't really want to use different notations for discussions in Japanese and English. When you see x = a(f), you'll get slightly confused.
  * No one can read it 
    * There's no such thing as mathematics only for certain language community.
  * Latin alphabets are more suitable for notating with a single letter. 
    * 「か」 for 函数 really isn't appealing for me because it loses so much information. `函（変）= 正弦(変) + 2` looks interesting, but we can't have two variables (Kanji don't have natural succ/pred). 函(変1, 変2) = 変1× 変22 might be worth discussion. There's no practical benefits, though.
  * I have never been told _not_ to Japanese characters specifically. We just learn from what are widely used and stick with them, because that's the easiest for communication.

So I believe the answer is

  * It's just because it isn't conventional to do so, and there aren't many reasons to do so, actually.
  * If certain conventions are established (I'm hoping 「よ」 for 米田 to be among the first), that character for that usage will be seen everywhere.

* * *

  * [Related question in Math.stackexchange](https://math.stackexchange.com/q/165368).
  * My finding on the 「よ」 is attributed to the following tweet:

数学記号として平仮名が使われる時代が既に訪れていたのか...
[pic.twitter.com/1MENyIDSwC](https://t.co/1MENyIDSwC)

-- ウニ (@unununum_1) [4 May
2017](https://twitter.com/unununum_1/status/860125300104937472?ref_src=twsrc%5Etfw)

