10 ms·

Using Emojis in Mathematical Notation

24 points by rmeertens 6y ago

uoaei 6y ago
emoji is both the singular and plural form of the word.
- pmiller2 6y ago
  And, English grammar is rightly descriptive rather than proscriptive. Today's nonstandard usage is tomorrow's standard English.
techwizrd 6y ago
I 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 6y ago
  Depends 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.
a-nikolaev 6y ago
Many 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 6y ago
  If 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_historic_currency_symbols https://en.wikipedia.org/wiki/Currency_symbol#List_of_histor...
  - a-nikolaev 6y ago
    Yeah, there is a lot of interesting symbols to use.
definetheword 6y ago
I don’t know, my initial thought is that it’s fairly distracting and makes me pause longer to think. Anyone sensing the opposite?
partingshots 6y ago
This is great; emojis to entice younger generations into the world of math. I love it!
notRobot 6y ago
Yeah, 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 https://news.ycombinator.com/item?id=21760021 --- 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.
- taeric 6y ago
  It 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 6y ago
    Both 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.
shhsshs 6y ago
This paragraph convinced me: https://i.ibb.co/WsgQYHq/PNG-image.png https://i.ibb.co/WsgQYHq/PNG-image.png
zaptheimpaler 6y ago
kill me now yeet me to the astral plane
- pwdisswordfish4 6y ago
  Where all the emojises exist?
jhanschoo 6y ago
Emoji 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 6y ago
  My 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 6y ago
    I'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.
deleted 6y ago
[deleted]
deleted 6y ago
[deleted]
forgotpwd16 6y 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 6y ago
  I 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 6y ago
    Because 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 6y ago
      I 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.
AnonC 6y ago
This 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.
anordal 6y ago
Why is math restricted to single-character identifiers in the first place? energy = mass · lightspeed² ↑ As you would do in programming.
- TheGallopedHigh 6y ago
  Proofs can be very long, writing out full pages with single letters let alone full words would be difficult to parse
  - alexvoda 6y ago
    Source 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.
- heinrichhartman 6y ago
  That's perfectly fine, and sometimes done in expository writing. https://www.amazon.com/Algebraic-Geometry-Projective-Varieties-Mathematics/dp/3540586571 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 6y ago
    If 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.
- alexvoda 6y ago
  The 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 https://news.ycombinator.com/item?id=25207527
blackbear_ 6y ago
I 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-in-convolutional-neural-networks/ https://www.jefkine.com/general/2016/09/05/backpropagation-i...
heinrichhartman 6y ago
In 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 6y ago
  Math 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 6y ago
  I 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.
thomasahle 6y ago
Reading this in Firefox all I see is lots of [?] boxes. I almost thought the entire article was sarcasm until I looked through Chrome.
Zhyl 6y ago
I 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? [0] https://tauday.com https://tauday.com [1] https://betterexplained.com/articles/colorized-math-equations/ https://betterexplained.com/articles/colorized-math-equation...
- alexvoda 6y ago
  Never 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.
rambojazz 6y ago
This is just terrible to look at.

24 points by rmeertens 6y ago

uoaei 6y ago

emoji is both the singular and plural form of the word.

pmiller2 6y ago
And, English grammar is rightly descriptive rather than proscriptive. Today's nonstandard usage is tomorrow's standard English.

techwizrd 6y ago

I 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 6y ago
Depends 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.

a-nikolaev 6y ago

Many 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 6y ago
If 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_historic_currency_symbols https://en.wikipedia.org/wiki/Currency_symbol#List_of_histor...
- a-nikolaev 6y ago
  Yeah, there is a lot of interesting symbols to use.

definetheword 6y ago

I don’t know, my initial thought is that it’s fairly distracting and makes me pause longer to think. Anyone sensing the opposite?

partingshots 6y ago

This is great; emojis to entice younger generations into the world of math. I love it!

notRobot 6y ago

Yeah, 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 https://news.ycombinator.com/item?id=21760021 --- 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.

taeric 6y ago
It 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 6y ago
  Both 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.

shhsshs 6y ago

This paragraph convinced me: https://i.ibb.co/WsgQYHq/PNG-image.png https://i.ibb.co/WsgQYHq/PNG-image.png

zaptheimpaler 6y ago

kill me now yeet me to the astral plane

pwdisswordfish4 6y ago
Where all the emojises exist?

jhanschoo 6y ago

Emoji 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 6y ago
My 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 6y ago
  I'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.

deleted 6y ago

[deleted]

deleted 6y ago

[deleted]

forgotpwd16 6y 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 6y ago
I 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 6y ago
  Because 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 6y ago
    I 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.

AnonC 6y ago

This 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.

anordal 6y ago

Why is math restricted to single-character identifiers in the first place? energy = mass · lightspeed² ↑ As you would do in programming.

TheGallopedHigh 6y ago
Proofs can be very long, writing out full pages with single letters let alone full words would be difficult to parse
- alexvoda 6y ago
  Source 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.
heinrichhartman 6y ago
That's perfectly fine, and sometimes done in expository writing. https://www.amazon.com/Algebraic-Geometry-Projective-Varieties-Mathematics/dp/3540586571 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 6y ago
  If 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.
alexvoda 6y ago
The 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 https://news.ycombinator.com/item?id=25207527

blackbear_ 6y ago

I 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-in-convolutional-neural-networks/ https://www.jefkine.com/general/2016/09/05/backpropagation-i...

heinrichhartman 6y ago

In 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 6y ago
Math 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 6y ago
I 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.

thomasahle 6y ago

Reading this in Firefox all I see is lots of [?] boxes. I almost thought the entire article was sarcasm until I looked through Chrome.

Zhyl 6y ago

I 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? [0] https://tauday.com https://tauday.com [1] https://betterexplained.com/articles/colorized-math-equations/ https://betterexplained.com/articles/colorized-math-equation...

alexvoda 6y ago
Never 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.

rambojazz 6y ago

This is just terrible to look at.