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So I am in a dilemma in that a recent publication literally has used up every (legible) character on this page. We have checked thoroughly and every single character is necessary and this many characters are unfortunately needed to avoid confusion (This is what happens when you try to combine several different theoretical areas together). We have also used up a bunch of symbols such as stars or dots. This question is not about how I should reduce the number of characters.

So right now I am thinking of using characters from outside of the European family, such as Japanese characters (Hiragana/Katagana) or Korean or Chinese. Of course, provided that these characters are simple enough. Some candidates include ひ, と, ㅈ, ㄹ, し, 十. Some of these characters are quite suitable and have simple pronunciations, although we are not thinking of pronouncing them in presentations.

But I have two concerns:

  1. most conferences and journals have a "We only accept submission in English" rule: The submission must be written in English. Does this violate that policy?

  2. does using these character violate some sort of implicit cultural norm in scientific writing and European/North American conferences so that we should avoid it?

Update:

Thanks for all the feedback. But most seem to focus on what other fonts I should try to use instead. Just as a clarification, in my area it is highly not uncommon for the papers to use many many symbols. Here is a mild recent example (not affiliated with these authors) and this one I saw that made me go "wow the notation is so nice!" (again, not affiliated). These seem to be conference submissions (around 10 pages). For full submission it can go up to 20-40 pages. So as you can imagine a symbol problem quickly arises.

I can't help if everything comes out like this. If you notice, it is easy find usage of thing such as $a^{i,j}_{k,l}$. k, and l are two agents from i and j graphs and a is just one possible variable out of many variables. So we are already making heavy use of super/subscripts. We use hats to denote estimated values so we are already there as well. We are also making use of mathcal, mathscr, mathbf, mathfrak, texttt, etc. to denote sets, graphs, matrices, special matrices and special conditions respectively. All extremely conventional usages.

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    I moved to chat a number of comments partially answering the question or suggesting alternatives. Please read this FAQ before posting another comment.
    – Massimo Ortolano
    Jun 28 at 17:47
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    I am confused by the update. None of the two papers you link to seem to have an unusual amount of symbols. Iin fact I think most of my papers have many more, and I never risked to run out of them. Jun 28 at 19:02
  • @DenisNardin 1. This is not a competition :), 2. I have mentioned already that these papers are "mild" and "nice" examples (look at the dates of these pre-prints: I grabbed them on the fly), and 3. I am not lying about running out of symbols and made this question for fun. Jun 28 at 21:56
  • Also I'm seriously looking at these comments and weighting them in. Also thinking about simply cutting out some symbols. Jun 28 at 22:01
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You’re doing it wrong, and are already violating a cultural norm that’s much more important than any norm having to do with a specific choice of character set.

That cultural norm is: write papers that can be understood by other people.

If you are using all the characters in the Latin and Greek alphabets, and dots and stars and a bunch of other symbols so that you literally ran out of symbols to use and still need more, I am willing to bet that your paper violates this norm in the worst possible way. If you add even more characters from other character sets most people in the West are unfamiliar with, you will only be digging your paper deeper and deeper into a black hole of incomprehensibility.

Aside from this, the answer to your two more specific questions are “probably” and “yes”, but I would classify those concerns as secondary compared to the one I mentioned above.

Bottom line: if Andrew Wiles was able to prove Fermat’s last theorem, Perelman proved the Poincaré conjecture, and countless other mathematicians and computer scientists successfully publish groundbreaking new results all the time with “only” the Latin and Greek alphabets and standard mathematical symbols at their disposal, I’m confident you too could expound your theory with those resources. So I suggest rethinking the approach behind your question and asking yourself why you need so many symbols when everyone else doesn’t.

Edit: another couple of observations about your suggestion:

  1. The Unicode standard, widely accepted as the ultimate in standardization of text representations, defines what is a mathematical symbol, and has several dedicated blocks for those symbols (with certain standard symbols falling in other blocks for historical reasons, but still being classified as mathematical). Your idea would pretty clearly go against the spirit (if not the letter) of that standard.

  2. Your idea would also go against the increasingly common idea of taking accessibility, and the needs of people using screen readers and other accessibility software, into account in writing and publishing. Admittedly this is also a problem with existing mathematical writing, but your idea would certainly make things even worse than they already are for (for example) blind readers.

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    Using symbols from outside the mathematical operator blocks is not a "violation" of the Unicode standard. (+ is not in any mathematical block, and the upright letters used for things like \sin are also not strictly mathematical - they're the same characters you type with every day!) Blocks are just the general way that the characters are organized, not any sort of prescription on how the characters are used.
    – Deusovi
    Jun 26 at 16:26
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    A "violation of the Unicode standard" would be using, say, an invalid byte in a UTF-8 string, or a font that switches φ and ϕ. Unicode describes which characters are used, and notes that other characters are often used as well [see the bottom of page 5, which explicitly gives の]. Unicode does not set any standards for how you write, only for how that writing should be encoded.
    – Deusovi
    Jun 26 at 17:05
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    unicode.org/versions/Unicode13.0.0/UnicodeStandard-13.0.pdf Page 44: "The normative status of blocks should not, however, be taken as indicating that they define significant sets of characters. For the most part, the blocks serve only as ranges to divide up the code charts and do not necessarily imply anything else about the types of characters found in the block. Block identity cannot be taken as a reliable guide to the source, use, or properties of characters, for example, and it cannot be reliably used alone to process characters."
    – Deusovi
    Jun 26 at 17:05
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    Unicode does not standardize mathematical writing any more than it does nonmathematical writing: when, say, new Chinese/Japanese characters are created, it expands to be able to encode them, rather than prohibiting them. The standard is for how you should encode writing, not for what you're allowed to write in the first place.
    – Deusovi
    Jun 26 at 17:35
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    As a software engineer, I find the reference to Unicode laughable. The whole point of the Unicode standardization process is that it follows common usage. It does not define common usage. If a significant number of people have ever used a given character for serious purposes (i.e. not something like Klingon or Elvish script), and the Unicode consortium is aware of that fact, then they will generally encode that character. They do not go around telling people which characters to use.
    – Kevin
    Jun 28 at 8:51
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In mathematical writing, it is common to use variants like these:

examples

and possibly others

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    Don't forget accents, so easily hundreds of options. Jun 26 at 4:29
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    Good point, although I must admit that I find script and fraktur difficult to read at a glance.
    – J W
    Jun 26 at 9:05
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    "Difficult to read" ... but not more difficult than と, ㅈ, ㄹ, etc.
    – GEdgar
    Jun 26 at 11:04
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    Fair enough. I should clarifying that I wasn't comparing with "と, ㅈ, ㄹ, etc.", just making a remark about my own experience.
    – J W
    Jun 26 at 11:53
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    Luckily capital greek letters are rarely used .... :-)
    – lalala
    Jun 26 at 19:03
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If you really run out of symbols, I would try a different path.

In software development, people name everything by just using ASCII characters: They use words instead of single letters.

I know that in mathematics, you usually don't do that. But on the other hand, calling the cost variable cost instead of c will not make the paper unreadable.

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    In fact I’d argue that software is more readable for precisely the reason that we use full words with actual meaning. I find mathematics hard to understand because I have to look up the meaning of symbols all the time.
    – Michael
    Jun 27 at 12:38
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    The way mathematics is written established itself when people mostly wrote by hand. When you have little space on a blackboard and you don't want to spend ages writing everything down, you tend to use short symbols instead of words. Mathematics is often very condensed. Jun 27 at 13:22
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    @Michael true, but there are other reasons why software is more readable. Programmers are incentivized by their industry to document their code and make it easy for other programmers to understand. They work in a more collaborative environment (often in large teams working on a project and needing to edit the same code base). Programmers and their industry also worked hard to come up with a set of good practices to facilitate good communication and collaboration. I guess you think more about such things when the difference between good and bad communication is many millions of dollars…
    – Dan Romik
    Jun 27 at 15:58
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    @Michael I don't disagree, however you shouldn't underestimate that maths often is harder to understand simply because it really is harder. A long mathematically formula will typically get even harder to understand if you make the variable names longer, even if they're more descriptive then, simply because of the further increased size. — What really helps for understandability is refactoring formulas into subexpressions, theorems into smaller lemmas, thereby making small variable scopes where it's quickly possible to look up the meaning. Jun 27 at 22:55
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    +1 Mathematics doesn't usually treat large problems in one sitting, so a terse formulation generally makes sense. In OP's examples, however, the math is basically describing a complex algorithm. Developers also started out writing terse code and, as you say, quickly learned that code which looks like math is impossible to maintain or read once the ecosystem grows into more variables that you can count on your fingers. A descriptive pseudocode does seem like a much better language for OP's problem, or at least for some subset of their problem.
    – J...
    Jun 28 at 11:40
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Use of non-Greek letters in the equations is not as uncommon as it seems. While the Greek letters are obviously the most popular, there are several commonly accepted symbols which are taken from the other alphabets, e.g.

  • Russian letter ш (sha) used in the number theory and Л (el) is used in some hyperbolic geometry,
  • Hebrew letter ℵ (aleph), ℶ (beth) and ℷ (gimel) denote aleph numbers, beth numbers and gimel function correspondingly,
  • Old english ð (eth) is used in context of derivatives,
  • Maltese ħ denote Planck constant,
  • Japanese よ (yo) is used in cathegory theory.

See this topic for more details. I myself have seen ℵ and ð being used in the papers and I am not working in any advances mathematics.

While there certainly are some drawbacks connected with readabilty of a paper written using excessive number of new symbols, there should not be any formal problems with the publisher as long as you can write all symbols in proper LaTeX script.

As the side note, there was a mistake (as pointed by @DanRomik) in this post with incorrect naming of the Hebrew letters, what quite well illustrates the danger of using new characters which are unfamiliar both to the autor and the readers.

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    Do you have sources for the representation of the Planck constant being of Maltese origin? He was German and according to Wikipedia, the variable name comes from a German word.
    – WoJ
    Jun 26 at 12:15
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    I think ð and ∂ are slightly different symbols. (If anything, ∂ looks more like the Russian cursive form of д, д.) But there's also よ for the Yoneda embedding!
    – Deusovi
    Jun 26 at 16:22
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    The letter you call gimel is a beth, and your beth is a gimel. A good illustration of the pitfalls of using unfamiliar character sets…
    – Dan Romik
    Jun 26 at 16:27
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    About $\partial$: from my amateur comprehension of the history of this, I think it is not "eth", but just some form of cursive "d", used deliberately by various people in the 18th century. Also, I'd suspect that Dirac and others just put a slash through an "h" as a sort of modifier/accent, rather than consciously adopting a Maltese letter. Jun 26 at 18:44
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    You need to distinguish between the optical representation of a character and how it is intended or interpreted. If a φ is used in mathematical literature, we pronounce it phi and this dates back to the tradition of using Greek letters because they were familiar to most readers at that time. If an ℏ is used in physical literature, we pronounce it h bar (not ħe) and this originates modifying the letter h used for a similar constant. I see no reason to assume that this is or was ever thought of as a Maltese character, even in the unlikely case that the typesetter used a Maltese glyph.
    – Wrzlprmft
    Jun 28 at 16:26
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Even with a symbol list, keeping track of so many different letters will be difficult for readers. It can be made easier by introducing order and hierarchy to the symbols.

The style will vary by field, but for example you could have:

  • Uppercase letters A, B, ... for main symbols that link together the whole work and appear in multiple sections.
  • Subscripted uppercase letters Ax, Bc, ... for symbols that are related (but not equal) to one of the main symbols.
  • Lowercase letters a, b, ... for local parameters, which can then be reused for different purposes in different sections.

That still leaves a lot of symbols available for other purposes. For readability, you should make use of the same symbols and conventions that other papers do, within reason.

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    How about subscripted letters where the subscript is a descriptive word. I'm thinking $\lambda_\textrm{min}$ and $\lambda_\textrm{max}$. I think this is a great way to make it clear the subscript is not an index.
    – Clumsy cat
    Jun 26 at 16:41
  • @Clumsycat We are in fact already there. The two examples are currently being used to denote maximum and minimum eigenvalues. Again standard in the literature. Jun 28 at 21:58
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Apart from the other answers that a paper using so many symbols will be incomprehensible (I do entirely support these answers): many publishers use commercial custom fonts and their fonts may simply not contain characters for scripts other than latin and greek.

Even European scripts such as cyrillic cause problems. See what happened here, for example? All of the text is in Times, yet the Russian abstract is in Computer Modern: https://doi.org/10.1016/j.hm.2020.04.003

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You should definitely use those characters. Academia needs to be less Eurocentric.

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    The primary goal of a paper is to be understood, not make a geopolitical statement. Papers used to be written in French and in German before they were mostly written in English. Cultural norms do vary over time. Still, papers should be understood, and I don't think many people would understand a paper containing every Latin and Greek symbols, and some Asian ones for good measure. Jun 26 at 9:21
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    And to be thorough let's use every single symbol ever invented by every culture chosen randomly, you know, to commemorate world history.
    – Passer By
    Jun 26 at 18:26

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