# Why are Japanese characters not used in equations?

Why do Japanese texts/scientific articles not use kana/kanji in their equations? For example

f(x) = x + 1


f(あ) = あ + 1


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"

• I can only speculate, but it's just that much of the conventions used in scientific or mathematical body of knowledge have been based on Western notations. For the sake of understanding and simplicity they could've stuck to the same symbols. – keithmaxx Sep 27 '17 at 8:27
• Probably there were no concept of western “function” in Japanese arithmetic until the notation was imported into Japan. Ex) 和算と関数 m.chiebukuro.yahoo.co.jp/detail/q11101327326 – user25382 Sep 27 '17 at 8:39
• – user25382 Sep 27 '17 at 9:45
• @kimiTanaka 数学専門ですね。詳しい情報、素晴らしいです。（個人的には鼻血出ますが。） kimiTanaka's link contains comprehensive explanation (in Japanese) so you might want to refer to that. The English version page, on the other hand, is lacking. – keithmaxx Sep 27 '17 at 11:34
• I'm sorry, I cannot read Japanese that well yet, I would be happy if someone would state the main idea behind kimi Tanaka's link in English..? – Stephan Sep 27 '17 at 12:26

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:

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

Elaborating on this,

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”, page 13, they have this notation: "The Yoneda embedding よ : C → P(C)" (No \mathcal shown here)

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. 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.

— ウニ (@unununum_1) 4 May 2017
• To summarize: "We could, but why?" – Yosh Sep 28 '17 at 5:20
• 細かい話ですが、長方形の縦はlength でしょうか。en.wikipedia.org/wiki/Height In elementary models of space, height may indicate the third dimension, the other two being length and width. Height is normal to the plane formed by the length and width. – user25382 Sep 28 '17 at 22:49
• @kimiTanaka ありがとうございます，length 使うのは初めて知りました．Height も用例はあるようですが（感覚的にですがプログラミング界隈ではこっちをよく見る気がします． javascript api とか），自分で調べてみても length のほうがより普通のような感じですね．修正しました – Yosh Oct 5 '17 at 2:46
• Using that fillrect method you can change the width and the hight as you like and you can cange the shape like a building. Probably the height is also used in altitude of a triangle and a parabola in x-y cartesian cooradinates. – user25382 Oct 5 '17 at 3:38

In Edo Period, Algebraic equations of three unknown variables were stated in the following expressions.

There exists a right triangle(勾: x 股: y). Now, 勾再自乗数(x^3)と弦再自乗数(弦: hypotenuse z^3)と相井せて共にー百五十二寸(152) (x^3 + z^3 = 152)。股再自乗数(y^3)と弦再自乗数(z^3)と相併せて共にー百八十九寸(y^3 + z^3 = 189)。勾股を問う(What is x, y?)

As for the function, I saw some say one of the concept(ex: hit something into the black box and you get some outcome) was imported into Japan in Edo Period with the word(関数）.

Bonus

Yosh’s answer is very specific. I found japanese mathematician says an American mathematcian used for mathematical symbol.(https://mobile.twitter.com/FumiharuKato/status/860438562415628288)

N. KATZ. Nilpotent connections and the monodromy theorem : applications of a result of Turrittin. Publ. math. IHÉS, 39 (1970), p.175-232

• According to this tweet, twitter.com/FumiharuKato/status/860822164382990336, 　　　A Japanese mathematician also states ”ひらがな”　or "カタカナ”　can be used as a mathematical notation in the future like Cyrillic or Hebrew since it's phonogram. – user25382 Sep 28 '17 at 10:49