Hacker News Reader

Comment by nitrogen | Hacker News Reader

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.

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?

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?

[0] https://news.ycombinator.com/item?id=29899938

View on HN

I think this is very useful for presentations (I wish there was a mathml version) and books. The issue with using this for articles is that most journals (at least in my field) have tight page limits, while this uses quite a lot of space. So using these annotations would mean cutting down significantly on the rest of the paper, which would likely degrade readability.

How would this help you? Now these explanations are just in the paragraph next to the equation and are not limited to 3 words.

> Now these explanations are just in the paragraph next to the equation and are not limited to 3 words.

Not necessarily. Will Crichton, a PhD student at Stanford University, has been working on a tool called Nota [0] that he's hoping might serve as a platform for online paper publication. I'd suggest checking out the initial presentation of Nota [1] to see some ideas of how syntax highlighting-type effects can be made as toggle-able capabilities that are not intrusive nor dislocated as you suggest.

[0] https://nota-lang.org

[1] https://willcrichton.net/nota/

It activates more information channels into my brain.

Prose is just one transfer channel, and for me, not a very efficient one (though I love reading!). Mathematical notation is one more.

But that leaves out word association, color, spatial relationships, conceptual graphs, diagrams, etc. The more channels I can activate, the faster I can build intuition, and intuition facilitates practical application.

Here's an example of how I like to use color from my own modest work: https://youtu.be/iyjIVSnrPSo?t=424

Another example: https://youtu.be/iyjIVSnrPSo?t=345

In this case, each independent variable in the equation gets its own color, and that color corresponds to a label on the graph above. The imaginary unit also gets a special color, which matches the color of its definition, for those of my audience who are unfamiliar with or out of practice with complex numbers. And the syntactic elements are muted to make the shape of the equation "pop" for those whose eyes are not routinely trained to read math notation. Elsewhere in the video I use different colors to represent positive, negative, and zero frequencies.

So to restate, it's all about giving information as many paths into my brain as possible.

As an engineer translating formulas into code, I'd rather go and get the deep and clear understanding of the meaning behind the formulas, rather than rely on a highlighting to help me away with the vagueness of my understanding.

Does the average mathematician have any incentives to create easily understandable explanations for their equations and algorithms? Ones that engineers can use to implement various ideas.

The average mathematician does not work on anything engineers would care about. Maybe you are talking about CS professors instead of mathematicians? I've noticed that many here on HN mix the two. They aren't the same, CS professors aren't specialists on math, they use math as a tool and often don't understand it well enough to explain it properly in a paper. Not to mention that repeating the same explanation in every paper creates a lot of redundancy, the material is already much better explained in many books or online.

It depends on the CS professor and university. At U of Waterloo, for example, there are two separate degrees one can get as a CS major. One that's a BMath, the other as a BCS. I studied engineering (BASc) there, and while the website may say otherwise[0], everyone recognized that the BMath was the more serious of the two degrees even if there were exceptions here and there. Anyway, all of this to say that mathematicians and computer scientists are highly related. Even more so than mathematicians and physicists. They both deal is pure, (usually) computable abstractions.

[0] https://cs.uwaterloo.ca/current-undergraduate-students/major...

It's definitely advantageous if you can claim that people in industry are using something you invented (and in other fields I'm more familiar with there are a lot of consulting opportunities)

Reply on news.ycombinator.com