From comments here it sounds like people already deeply familiar with the mathematical notation used in a domain really want to stick with the compact, black-ink-only equation representation. However, as an engineer who occasionally wants to translate papers from a mathematical field I rarely encounter into code I will use all the time, annotations like this would greatly increase the utility I could derive from a paper in a given amount of time.<p>Also, as yunruse mentioned in [0], and as I have done in my own videos that include math, syntax highlighting for math is very useful for absorbing new math. How acceptable would that be to practitioners already deep in their fields?<p>So, could annotations of this form be acceptable to both groups if they were switchable on or off in an online version of a paper?<p>[0] <a href="https://news.ycombinator.com/item?id=29899938" rel="nofollow">https://news.ycombinator.com/item?id=29899938</a>
For many of the papers I read (engineering) I would love to be able to click on symbols in an equation and have it link me back to where that term was first defined in the paper, either in another eqn or in the text. Tracing back in this way is a major pain point e.g. when trying to reproduce calculations. Seems like something journals/latex could easily implement in an automated fashion (maybe already possible?)
Tangentially, one of the things I always enjoyed seeing in the wild was semantic colouring in equations. The educational YouTuber 3Blue1Brown [0] and to some extent the maths side of YouTube in general tend to make use of them, colouring like terms the same to give a subtle visual aid, similar to pretty printing.<p>[0] <a href="https://youtube.com/3blue1brown" rel="nofollow">https://youtube.com/3blue1brown</a>
I definitely see value in this, but it's currently too much of a hassle to use. It requires lots of tedious code duplication and requires the user to manually set positions and lengths for the arrows and annotations, defeating the purpose of allowing writers to focus solely on the content of their work. However, this would be a great thing to try to encapsulate in a package.
I was reading Russian political Telrgram earlier today, and one of the better channels ("Толкователь") had a post about a scientific study on why people prefer conspiracy theories over scientific information.<p>The study's summary says that this is because conspiracy theories are communicated in a language that is understandable, while scientific communication uses language that is opaque for most people.<p>Which leads me to the conclusion that any effort towards making scientific communication more understandable to general public -- including the annotated equations -- is a good thing.
Mathematics seems to be obsessed with one-liners<p>Single letter variable names (often from different alphabets) and complex expressions that should be broken down would never make it through a code review ;-)
While I like the annotations, I have to say they make it difficult to make out the original equation. It parses and highlights variables and gets in the way of seeing a cohesive whole equation.<p>I think an annotated version would be good as a supplement.
I always wondered why no one is doing syntax (or, semantical) coloring/highlighting for stuff like mathematics or sheet music. It could even help with simple plain text.<p>The reason is probably that "it's always been like that", just like keyboard layouts. Though one could argue that coloring would be not be very disruptive and backwards-compatible, so it wouldn't hurt traditional reading much.
Rendering the different symbols in different colors might be enough, as long as those colors are used in the text defining the symbols. Used sparingly (i.e. only for the symbols that are relevant to the argument), it can greatly enhance readability.<p>I feel like these annotations go slightly overboard; the entire equation/annotation construct is visually pleasing, but hard to parse.
Seeing this presented for use in papers is a very good thing. These annotations look alot like slides many people make (sometimes showing relations between multiple equations, etc). However, much of this readability is customarily stripped out for the sake of uniformity. I think most journals im familiar with enforce specific formatting for equations.
Definitely something that could be nice in an active-document.<p>By analogy, Wikipedia articles have a feature where, if you mouse-over a link, it'll display a preview of the link-target (<a href="https://en.wikipedia.org/wiki/Wikipedia:Tools/Navigation_popups" rel="nofollow">https://en.wikipedia.org/wiki/Wikipedia:Tools/Navigation_pop...</a> ). This can be an efficient way for a reader to conveniently glance at the definition of a term while reading.<p>Mathematical notation varies significantly between fields, and many papers define custom symbols with their own paper-specific definitions. So this sort of feature isn't just something for math-newbies, but rather something that could significantly benefit experts too.<p>The same sort of annotations might be more situational in non-active documents, where there'd be more of a trade-off between helpful-annotations and clutter.
TBH, I don't think the annotations add anything. You can simply write<p>"
Lap(x | mu, b) = ...<p>where b>0, a scalar parameter.
"<p>What is needed is some better way to motivate the concepts behind any maths that is confusing for people who might be confused.
Here are the examples in long-form rather than a tweet:<p><a href="https://github.com/synercys/annotated_latex_equations" rel="nofollow">https://github.com/synercys/annotated_latex_equations</a>
Finally! This is super useful! I wanted to do stuff like this ten years ago for small code samples but didn't get very far with TikZ. Doing it for equations is even more complicated to get into a pleasent shape, I guess.
On one hand I like this, and have used similar visuals in presentations, on the other hand I feel it's a less a problem related to math literacy per se, and more needing a workaround relating to the artificial limits and style restrictions imposed by journals (as well as the limitations of a paper medium, to some extent).<p>The whole "pay £1000 per extra page" by itself has been enough to reluctantly cause me to cram math inline and assume symbols are known to the field without too much explanation.
I understand math is optimized for writing, but honestly I've always felt it would be better if we just used long variable names instead of single letters.
I’m not sure I understand what the point of this is.<p>If I’m reading academic papers on a particular topic then I already know the notation the math is written in.<p>If I’m reading a paper outside of my field then I’m not really interested in the details of the equation but more of its application and what it means.
I don't think I like this as a replacement for simply defining terms in the text. You could do both but something like "S a subset of Range(X)" when the equation is about the probability that X is in S doesn't seem important enough to take that prominent a position in the equation.<p>I can see this style of annotation it being helpful when you need to add some context or want to explain a pre-existing formula.<p>And I can definitely see this being used to highlight key ideas during a tricky derivation, stuff like partial integration could be a lot neater if you can point out the part of the equation that you're partially integrating.