Equivalent question: What Chinese letters won't equal 1? (If I need to specify, then I guess I'll pick Mandarin)

From: the homophonic group: a mathematical diversion --> This is an exercise from Michael Artin's Algebra on, well, abstract algebra. In this exercise for the English language, words are equal if they are homophones, kind of like a formalisation of the joke that sin(x)/n=6. So in English:

bee=be --> This implies e=1 by cancellation of b and e.

buy=by --> This implies u=1 by cancellation of b and y.

rase=raze --> This implies s=z by cancellation of r and e.

canvass = canvas --> This implies s=1 by cancellation of c,a,n,v,a and s. By canvass=canvas and rase=raze, we have s=z=1.

Eventually, all 26 English letters will equal 1. Apparently, this was done for French and Czech.

  • 1
    How do you mathematical wise cancel a written glyph?
    – mootmoot
    Commented Aug 16, 2018 at 16:29
  • 1
    First of all, Chinese writing is not phonetic. If by "Chinese letters", you mean the letters used in Pinyin, then all homophones are spelled exactly the same, because the whole system is designed to reflect the pronunciation. This is different from a phonetic writing system where the written and spoken languages may have evolved over a long period of time (with certain elements more resistant to change than others) and you end up with things like different spellings for the same sound or different sounds for the same spelling.
    – monalisa
    Commented Aug 16, 2018 at 22:27
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    Humoring your (math and barely language related) question: If you use pinyin, it's a perfectly phonetic alphabet. Homophones always have identical spelling, so you won't be able to collapse anything down to 1 (if I understand the problem correctly). If you write out words in Chinese characters, you can end up with some relations like 皇=黄, which will lead you to have some equivalence classes of size >1. But I don't see how you could ever get a 1--that seems to require homophones written w/different numbers of characters, which is impossible. Commented Aug 17, 2018 at 0:08
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    There is no hanzi alphabet.
    – fefe
    Commented Aug 17, 2018 at 1:30
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    @BCLC "What's the hanzi alphabet?" Hanzi has no alphabet because as I said in previous comment, Chinese writing is not phonetic, and only phonetic writing systems use alphabets.
    – monalisa
    Commented Aug 17, 2018 at 3:02

4 Answers 4


Chinese writing works differently, of course, to alphabetical writing.

  • If you define the basic unit of written Chinese as the character, then no Chinese character will equal 1, because there's no such thing as a silent Chinese character.*
  • If you define the basic unit of written Chinese as a stroke, then the homophonic group is trivial and is just the group comprising all strokes.
  • If you define the basic unit of written Chinese as all unicode-encoded decompositions (this is not a natural way of decomposing the written language), then non-1-value characters can be found by searching through a database for characters which aren't part of any other character. Examples can be found by Googling search terms like "CJKV Characters with the most strokes".

*I suppose if you wish to reduce expressions like "Aaaaah! (啊啊啊啊!)" then you could plausibly say that 啊 = 1...

  • what about pinyin? is that the 3rd bullet point?
    – BCLC
    Commented Apr 10, 2021 at 11:51

Your question talks about "Chinese letters". You need to clarify what you mean by "Chinese letters". The Chinese writing system is not phonetically based and has no alphabet as such.

If, by "Chinese letters", you are referring to the letters used in Pinyin (or any Romanization system for a Chinese dialect), then all homophones are spelled the same, and your method of cancelling out identical letters in homophones will not work, since all letters will be cancelled and there will be nothing left.

Languages with a phonetically based writing system have evolved over time, with certain elements more resistant to change. As a result, there are cases of multiple spellings for the same sound, and multiple sounds for the same spelling.

Pinyin is different. It is designed to help speakers to sound out the written characters, which is not phonetically based. With such a purpose, if the pronunciation of a written character should change, the spelling will also change to reflect that. All homophones are necessarily spelled identically, without exception.

I do not believe your homophonic group exercise will work on a non-phonetic writing system.

  • The last line is because there is no identity? Thanks monalisa!
    – BCLC
    Commented Aug 18, 2018 at 0:03

There are few technical questions you need to deal with before you try to map it mathematically.

  1. Chinese glyphs itself is an abstract symbol, it doesn't tie with the speaking language. For example, the glyph 永,can be pronounced in many different dialects with, i.e. jun3 jun1 yun1 yung1 jun3 jun3 run3 jun3 wing5 iong2 uêng2

  2. Strokes of the Chinese glyph. There are 8 basic strokes, 28 sub-strokes.

  3. Due to no.1, many glyphs shared the same pronunciation. Even if you choose Pinyin alone, it just doesn't work.

  4. Chinese society pronounces each glyph individually. Mixing with fact no.3, you will notice it take a huge effort to change the habits. This required a totally new form of language structure.

One main ambition of the China communist party promote the use of Pinyin, is to Romanise Han-speaking. It stopped at the Romanize pinyin standard and go no further.

Due to the big difference in language structure, I doubt you can use the homophonic grouping.

(update) Perhaps the best analogy for the Chinese glyph speech and writing separation is the mathematic symbol. For example, the delta δ, it as nothing to do with the language spoken, it is a kind of abstraction.

  • You mean there is no identity and therefore not a group? Thanks!
    – BCLC
    Commented Aug 17, 2018 at 9:33
  • @BCLC what do you mean "there is no identity" ?
    – mootmoot
    Commented Aug 17, 2018 at 9:49
  • any group must have an identity soooo if nothing cancels in what would be the Chinese homophonic group, there is no identity in what would be the Chinese homophonic group and thus no chinese homophonic group
    – BCLC
    Commented Aug 17, 2018 at 9:51

interesting question, here's a cantonese-driven approach:

in recent decades, there's a trend to de-compose chinese character (漢字) into components (部件). the 中央研究院文獻處理實驗室 suggested there're 1316 basic components.


next, the cantonese pronunciation juet3 has these characters:



剟 = 啜

this implied 刂 (u+5202) = 口 (u+53e3), by cancellation of 叕 (u+53d5)

綴 = 輟

this implied 糸 (u+7cf8) = 車 (u+8eca), by cancellation of 叕 (u+53d5)

and then, what can i conclude here?

sorry for the termination here, cause my mathematic is not good enough :)

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