Using Emojis in Mathematical Notation
24 points by rmeertens 4 years ago | 72 comments- notRobot 4 years agoYeah, no. Please don't do this. This has been discussed previously w.r.t commit messages, and I'd argue that the reasons for not doing so with maths are largely the same: https://news.ycombinator.com/item?id=21760021
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They're bad for accessibility. Don't work with screen readers . Hard to make out for people without perfect vision. Harder to type out.
They don't render well on many systems. They can't be handwritten. How are they do be pronounced? "croissant emoji squared plus girl wearing hat"?
Conventions exist for what symbols to use where in science and math. Don't mess with this. Kids won't magically find math easier if you use emoji in place of symbols.
Instead, please focus your efforts of improving teaching methods.
- japanuspus 4 years agoAlso, emojis are hard to write by hand, which is an important feature to some people.
I find it very hard to internalize math without going through the derivations with pen and paper. Though I must admit that I have slowly gotten to the point of preferring to proof-read calculations for publication by typing out the intermediate steps in latex and then commenting them out.
- SiempreViernes 4 years agoLet the person who can write a decent \xi make the first claim that all greek letters are easy to write...
- pmiller2 4 years agoHuh, aren't \xi and \zeta just "squiggle" and "squiggle with a loop"? :P
- pmiller2 4 years ago
- SiempreViernes 4 years ago
- thaumasiotes 4 years ago> How are they to be pronounced? "croissant emoji squared plus girl wearing hat"?
I knew a girl named 胡伊人 Hú Yīrén, who for a long time had her wechat display name as three emoji, a tiger face, a hand holding up one finger, and a human girl's face. (The intent would have been to read these as "tiger", "one", and "person", 虎一人 hǔ yìrén.)
But emoji didn't appear in notifications, and my phone was set to English rather than Chinese, so whenever I got a message from her the notification would read "[Tiger][No. 1][Girl] ...". I started thinking of her as "tiger number one girl", a bit.
- CJefferson 4 years agoI disagree. In maths, the main competition is Greek letters. Kids today arent going to know their eta from their gamma. I find many undergrads can't remember the Greek alphabet.
Sure, girl wearing hat might be a bad choice, but I think "simple emoji like tree, fire, snowflake (for example). Do a good job of replacing Greek letters.
Another place I use emoji, is for a set of Labella which should have no order. Mathematica a often say they are naming some things 1,2,3, but please forget the integers have arthmetic and ordering. If you use fire, tree, snowflake as the names, no-one assumes an ordering, or arithmetic.
- blackbear_ 4 years ago> Kids today arent going to know their eta from their gamma. I find many undergrads can't remember the Greek alphabet.
Not sure what is the problem here. Even without knowing Greek nor the Greek alphabet, its letters are sufficiently diverse and can be easily told apart.
I can understand emojis can make math more enciting for young children, but if high school+ people cannot get past foreign-looking Greek letters I doubt they would find the motivation to progress much further in understanding the concepts involved.
- CJefferson 4 years agoIn undergrad lectures I constantly have students refering to "fork" or "curly n", or just misnaming different Greek letters (and, I find myself sometimes doing the same). The Greek is (to me) unnessary block to discussion.
- CJefferson 4 years ago
- goto11 4 years ago> Kids today arent going to know their eta from their gamma.
Are you saying kids will not be able to distinguish between the two symbols? I highly doubt that. They may not remember the names of the symbols, but emojis have the same problem.
- CJefferson 4 years agoSorry, yes I mean they won't know how to say them out loud, which makes discussion hard, whereas they will know snowflake or fire.
Heck, I teach graph theory and I keep forgetting the damn names mid-lecture.
- alexvoda 4 years agoYes. You have to memorize the mapping between the meaning and arbitrary Greek letters whereas the meaning is more obvious with emoji. But both (greek letters, emoji) are bad solutions to a very stupid problem math has. See my comment here https://news.ycombinator.com/item?id=25207527
- CJefferson 4 years ago
- yorwba 4 years ago> Kids today arent going to know their eta from their gamma.
I was inclined to agree with you, but then I remembered the zodiac sign emoji. Capricorn is basically η with a looped tail and taurus is gamma ɣ with a bigger loop. I'm pretty sure kids wouldn't be able to write them by hand (neither would I), but they have the advantage that if you type their names on a phone keyboard, you just need to recognize the symbol and tap it. Maybe all that's needed for Greek letters to compete with emoji is equal treatment by keyboards.
- blackbear_ 4 years ago
- SiempreViernes 4 years agoOn the other hand, how much sense does it make to keep overloading the same finite set of ~50 symbols? And while the admonition to stick to convention is a good general rule, there are both places where there exists conflicting conventions as well as areas where no convention exist at all.
As for the criticism that emoji can't be handwritten or pronounced: show me anyone doing a proper xi, and ask the greek what they think of how foreigners pronounce their letters (or indeed how one pronounces bold face letters). Clearly these are problems that have been solved before, and so can be solved again to the same level of quality.
Further, when handwriting you really have far more freedom than when typesetting, I had a friend that taught me the useful shorthand of just drawing a sphere to indicate that the surface integral was over a sphere. I tend to name partial results things like boxes or triangles when I work out because lugging around a second or even third "a" is just not as clear. Importantly, it's also much more fun to call your partial integral "small house" than "iii".
All that being said, the example choices in the article seem like straight up bad choices: naming the sides of a triangle a specific direction seems unhelpful in the fairly common case of several triangles with opposite orientation for example.
- taeric 4 years agoIt is kinda ironic, in that one of my favorite math papers is Polya's On Picture Writing. Which seems to imply that math with pictures should work fine.
I can't disagree with you, though. Curious what makes it fine there, but bad here.
- alexvoda 4 years agoBoth have the same problem and Polya mentions it in his paper. Both are to various degrees incompatible with technology (printing press, keyboards, teletypes, text mode screens, CLI, screen readers, etc.).
The reason the printing press became so revolutionary in latin alphabet using countries even though paper, printing and movable type were invented in China, is because it is very easy to make a machine that uses it. The English alphabet is more or less a common denominator of all other latin alphabet-based languages. Any non-latin/greek/cyrillic script is very hard to adapt to the various forms of technology throughout history.
But both papers illustrate a very real problem. Mathematical notation is horribly, infuriatingly, idiotically overloaded. And, no, context is not enough to divine the meaning. There are plenty of examples where a symbol is used for multiple meanings in the same paper or the same lesson.
My opinion is that the cause of all these problems is a very brain dead decision in math to allow adjacency of symbols to signify multiplication. This results in no longer being able to use multiple character names for things (variables, constants, etc.). And this is crippling. It results in the use of modified characters as symbols, use of characters from other languages as symbols and now the proposal of use of emoji as symbols. Because why not, emoji are plentiful and are now easier to input, store and display than ever.
The same issue (diversity of names) was solved by almost all by having mandatory separator characters(space, tab, comma, semicolon, etc) that are not allowed in names. Imagine a programing language where it is impossible to tell at first glance the meaning of something like "TotalWeight". Is it one variable? Is it Total * Weight? Is it TotalW * eight? Is it Total * W * eight? Is it T * o * t * a * l * W * e * i * g * h * t? We can rewrite this last one as aeghilo(t^2)TW . This is mathematical notation. And it will not change because it is entrenched.
- SiempreViernes 4 years agoThis argument falls by simple counter example: cos, sin, log are all multi character names that are routinely used with no significant syntax confusion without having to use explicit multiplication indicators. So longer names are routinely used despite apparent impossibility due to multiplication confusion.
No, notation is terse for other reasons. Largely driven by the very common practice of writing it by hand. If you give your new object a long name and use that very name as a symbol you'll quickly discover that others who are interested will just abbreviate it to a letter to save effort writing it.
- CJefferson 4 years agoI'm going to be honest, there is a reason mathematicans drop multiplication (or in general, the most important operator in whatever you are working on), because it would double the size of basically everything you write.
In group and semi-groups, where there is only one operator, it would just produce "visual noise", but introducing a * between every pair of things you write down. I have done this in beginner classes, but it rapidly gets boring.
While I understand how it makes it harder to read for non-experts, when you are writing maths, and maths papers, as a job you don't want to double the size of everything and scatter *s around for no reason.
The best parallel I can think of (this isn't good, sorry) would be like attaching the type of every variable to every place you use it -- this would technically make it easier to follow a snippet of code, but create lots of visual noise.
- SiempreViernes 4 years ago
- alexvoda 4 years ago
- japanuspus 4 years ago
- techwizrd 4 years agoI think emoji would make it challenging for students. Students already struggle to decipher the handwriting and foreign notation of their professors. Adding emoji to that mix would make it even harder to keep up, and many emoji (and mathematical symbols, to be fair) are difficult to write down.
I would have struggled during my math and stats degrees if I had to distinguish between emoji and mathematical notation.
- samcal 4 years agoDepends on the medium people will use to do math in the future, there may be a material reason why handwriting is the main method, but I would say its just as likely that it goes the way of other, less structured texts as the tools get better.
It doesn't really matter if you can't write down an emoji if you don't write anything down.
- samcal 4 years ago
- forgotpwd16 4 years ago>Math is hard to understand.
Because of the concepts used.
>I have to translate every character back to the concept meant by this character
Using emojis for variables won't help with that.
>Every scientific domain has its usual notation for specific concepts
Does that imply each emoji be used for a single concept across all domains? Not only that won't be possible (considering people don't even always use same variable for something, e.g. Pythagorean theorem being a^2+b^2=c^2, α^2+β^2=γ^2, x^2+y^2=c^2, ...) but is also a bad idea even if it could work as it will imply you've to remember every single emoji used.
Again, math is about concepts not what symbol you use for a variable. Using emojis won't make anything easier to teach or to understand.
- beambot 4 years agoI find it ironic that your examples were single-character roman & greek letters. Why not Cyrillic? Phoenician?
I wouldn't use pictograms everywhere, but they could be elegant in certain contexts. E.g. having a dedicated pictogram for various base physics quantities (e.g. for mass, length, time, etc).
- qsort 4 years agoBecause the latin and greek alphabets are widely known and understood, at least an order of magnitude more than Cyrillic and at least seven orders of magnitude more than Phoenician.
This is like asking why I'm writing in English even though it's not my native language, I do that because almost every educated person understands English, while almost nobody would understand if I wrote in Italian.
Pictograms would be difficult to standardize and hard to reproduce, unless you commit to a small set of them, which would just become an alphabet in disguise.
- beambot 4 years agoI appreciate the Western convention, but a significant fraction of the world uses pictogram-like written languages (e.g. Chinese). Using pictograms to represent words or concepts isn't that far-fetched.
- CJefferson 4 years agoI'll willing to bet a significant chunk of the "emoji" alphabet is better known and understood than the Greek alphabet nowadays.
It is true you would have to stay in some reasonable-sized subset, and I can't begin to imagine the arguments if someone tried to define "common emoji" or something..
- beambot 4 years ago
- codethief 4 years ago> E.g. having a dedicated pictogram for various base physics quantities (e.g. for mass, length, time, etc).
What if you have two different lengths, one being the distance between two objects and the other being the position of the center of mass over time? What about their two masses? And, in relativity, their two proper times?
Now you're back to using subscripts and the Latin alphabet because what better way to describe the precise object you're talking about in a given language (here: English) than the language itself?
- qsort 4 years ago
- alexvoda 4 years ago>>I have to translate every character back to the concept meant by this character
>Using emojis for variables won't help with that.
Yes, they will, because there is an amount of meaning embedded in the graphical shape of the emoji used whereas there is none for a greek/chirillic/phoenician/etc. character.
But the real solution is to not limit names to a single character.
See my comment here: https://news.ycombinator.com/item?id=25207527
- beambot 4 years ago
- shhsshs 4 years agoThis paragraph convinced me:
- heinrichhartman 4 years agoIn my experience, math is 99% handwriting. You only put it into Latex once you solved the problem. Exploration and experiments are done on with pen and paper.
This is also the reason why notation is often terse, and highly domain/author specific. You get tired of writing long_variable_names very quickly if you do it OVER AND OVER by hand. Now think about how much work and confusion it would be to replace those symbols with little paintings...
- alexvoda 4 years agoMath exploration and experiments are done on pen and paper because the notation is incompatible with keyboards.
I assure you there is plenty of exploration done in tools like Jupyter.
- SiempreViernes 4 years agoI think this can just as well be an argument that this is all safe as it implies the only emoji used will be those that can easily be handwritten.
- alexvoda 4 years ago
- blackbear_ 4 years agoI need to see way more than Pythagoras' theorem to be convinced. Show me a couple of pages of "complex" concepts, with something like ten equations involving summations, triple indices and whatnot. Something like this [1] (no affiliation, first random thing I found). I bet emojis will make it even worse.
[1] https://www.jefkine.com/general/2016/09/05/backpropagation-i...
- Zhyl 4 years agoI feel this links quite closely to the 'Tau' debate around notation [0]. The idea behind using Tau is that it makes equations more easily relatable to Circles and highlights rotation where the concept exists. One of the cases for these emojis is to more easily highlight function of variables and to highlight the equation. Both of these are also along the same lines as coloured equations [1].
Something I strongly disagree with in both the Tau manifesto and this Emoji manifesto, is the notion that Tau and Emoji should be encorporated into the official literature. Pi is 'wrong' - always use Tau. Einstein's papers would be easier to understand if you used the fire emoji instead of E.
Of course not. But in the other hand, the responses to these arguments attack that aspect of the claim rather than the intent behind them. "You can't use Tau because all textbooks use Pi. You would need to reprint all textbooks in the world". "You can't use emoji because the support is bad, you can't draw them and you can't pronounce them."
What we're missing, and where all of these belong, is in a formal explanation format. Most attempts to break down and make concepts more palatable tend to be blogs, YouTube or even broadcast media. We don't see anything in between 'formal paper or textbook' and 'colourful diagram aimed at beginners'. Where are the colourful diagrams for your latest paper on Flat Chains in Banach spaces?
[1] https://betterexplained.com/articles/colorized-math-equation...
- alexvoda 4 years agoNever knew about colorized equations. That looks brilliant.
Thank you for connecting all these concepts together. And I agree that this is one of the hurdles preventing people from becoming more than beginners. We need a gentler progression in abstraction. For many people, learning math is like learning Vim.
- alexvoda 4 years ago
- definetheword 4 years agoI don’t know, my initial thought is that it’s fairly distracting and makes me pause longer to think. Anyone sensing the opposite?
- uoaei 4 years agoemoji is both the singular and plural form of the word.
- pmiller2 4 years agoAnd, English grammar is rightly descriptive rather than proscriptive. Today's nonstandard usage is tomorrow's standard English.
- pmiller2 4 years ago
- AnonC 4 years agoThis is definitely not universally readable (even for people with average eyesight) and looks like it won’t be for a long time. I skimmed through it and saw several lines filled with a series of [?][?] on a device with the latest available OS. I checked on another device (with a different OS) and could read the emoji replacements. The publisher may be excluding a large number of people with this method.
- jhanschoo 4 years agoEmoji in math has a useful niche, illustrating basic mathematics for young schoolchildren, and for simple recreational puzzles. Beyond this, the accessibility issues raised by others seem to be a greater concern to me.
- iNic 4 years agoMy physics teacher in high school would sometimes replace variables with smilies to make a point that the symbol representing the variable is not the thing itself and I think it helped some students who had problems solving the exact same equation with different variable names. Of course naming conventions are important and were mostly used, but the smilies always stuck with me for some reason.
- pmiller2 4 years agoI've done this, too, when teaching remedial algebra in graduate school. I'm pretty sure it helped some people, while not confusing those who were already confused anymore.
- pmiller2 4 years ago
- iNic 4 years ago
- thomasahle 4 years agoReading this in Firefox all I see is lots of [?] boxes.
I almost thought the entire article was sarcasm until I looked through Chrome.
- a-nikolaev 4 years agoMany math papers do use weird LaTeX characters [1], for example Halloweenmath [2]. And even though it does not look like there is a shortage of symbols for writing math, emoji can be used too, just be tasteful about it.
[1] http://tug.ctan.org/info/symbols/comprehensive/symbols-letter.pdf [2] http://www.ctan.org/pkg/halloweenmath
- throw0101a 4 years agoIf anyone writes a (sci-fi) novel and needs a fictional currency, some of those characters could be useful as an unit symbol.
Or go back in history I suppose (𐆖, 𐆗, ₶):
* https://en.wikipedia.org/wiki/Currency_symbol#List_of_histor...
- a-nikolaev 4 years agoYeah, there is a lot of interesting symbols to use.
- a-nikolaev 4 years ago
- throw0101a 4 years ago
- anordal 4 years agoWhy is math restricted to single-character identifiers in the first place?
energy = mass · lightspeed²
↑ As you would do in programming.
- heinrichhartman 4 years agoThat's perfectly fine, and sometimes done in expository writing.
https://www.amazon.com/Algebraic-Geometry-Projective-Varieti...
This get's very tedious to write if you use this over and over in proofs.
- runald 4 years agoIf you had to tediously write it over and over in proofs, why can't just you give it a name or an abstraction?
↑ As you would do in programming.
- runald 4 years ago
- alexvoda 4 years agoThe reason I found is because in math adjacency is interpreted as multiplication. There is no mandatory separator character.
See my comment here: https://news.ycombinator.com/item?id=25207527
- TheGallopedHigh 4 years agoProofs can be very long, writing out full pages with single letters let alone full words would be difficult to parse
- alexvoda 4 years agoSource code for software is much, much, much longer and structured in directories and version controlled and automatically syntax checked and automatically tested and even edited simultaneously remotely across the globe.
And in case of some languages we can even use the full Unicode for variable names (Julia). The only restriction is we have mandatory separators and adjacency does not automatically mean multiplication.
See for example VS Code Live Share for the last one if you are not aware of it.
- alexvoda 4 years ago
- heinrichhartman 4 years ago
- 4 years ago
- rambojazz 4 years agoThis is just terrible to look at.
- zaptheimpaler 4 years agokill me now yeet me to the astral plane
- pwdisswordfish4 4 years agoWhere all the emojises exist?
- pwdisswordfish4 4 years ago
- 4 years ago
- partingshots 4 years agoThis is great; emojis to entice younger generations into the world of math. I love it!